Finite Group DatabasebetaFinite Group Databasebeta| order | 30720 |
| isoclinism | isoclinic class of #72210099 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×#17309 ⋊ A5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72209709 |
| commutator, hypocenter | G | C1 |
| Frattini, socle | C25 | #11757162 |
| Fitting, cosocle | C2×#17309 | A5 |
| LCS | G | |
| UCS | C1 ◁ C2 | |
2662 conjugacy classes of subgroups; only the 6 normal subgroups are shown.
This group has 2662 conjugacy classes of subgroups — too many to draw. Only its 6 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(1,2)(3,11)(4,12)(5,13)(6,14)(7,10)(9,22)(15,31)(16,32)(23,38)(24,39)(25,34)(26,35)(27,36)(28,37)(29,40)(41,42)(43,46)(44,45)(47,50);(2,8,9)(3,6,15)(4,5,16)(10,21,29)(11,30,27)(12,33,28)(13,17,24)(14,18,23)(19,25,31)(20,26,32)(34,38,36)(35,39,37)(41,43,42)(44,47,45)(46,48,49)(50,51,52);(1,3,7,4)(2,10)(5,16,6,15)(8,17,21,18)(9,23,29,24)(11,12)(13,14)(19,33,20,30)(22,34,40,35)(25,27,26,28)(31,32)(36,38,37,39)(42,45)(43,47)(46,50)(48,51);(1,5,7,6)(2,10)(3,15,4,16)(8,19,21,20)(9,25,29,26)(11,12)(13,14)(17,30,18,33)(22,36,40,37)(23,28,24,27)(31,32)(34,39,35,38)(41,44)(42,45)(43,47)(49,52);(1,7)(2,11,10,12)(3,4)(5,6)(8,17,21,18)(9,25,29,26)(13,32,14,31)(15,16)(19,33,20,30)(22,38,40,39)(23,28,24,27)(34,36,35,37)(41,44)(43,47)(46,50)(48,51);(1,7)(2,13,10,14)(3,4)(5,6)(8,19,21,20)(9,27,29,28)(11,31,12,32)(15,16)(17,30,18,33)(22,34,40,35)(23,25,24,26)(36,38,37,39)(41,44)(42,45)(46,50)(49,52);(41,44)(42,45)(43,47)(46,50)(48,51)(49,52);(1,7)(3,4)(5,6)(8,21)(9,29)(15,16)(17,18)(19,20)(22,40)(23,24)(25,26)(27,28)(30,33)(34,35)(36,37)(38,39);(1,7)(2,10)(3,4)(5,6)(9,29)(11,12)(13,14)(15,16)(22,40)(23,24)(25,26)(27,28)(31,32)(34,35)(36,37)(38,39);(1,7)(2,10)(3,4)(5,6)(8,21)(11,12)(13,14)(15,16)(17,18)(19,20)(22,40)(30,33)(31,32)(34,35)(36,37)(38,39);(2,10)(8,21)(9,29)(11,12)(13,14)(17,18)(19,20)(22,40)(23,24)(25,26)(27,28)(30,33)(31,32)(34,35)(36,37)(38,39)34 conjugacy classes — view the full character table.
| maximal quotient of | #72266550, #72266551, #72266628, … |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((1,2)(3,11)(4,12)(5,13)(6,14)(7,10)(9,22)(15,31)(16,32)(23,38)(24,39)(25,34)(26,35)(27,36)(28,37)(29,40)(41,42)(43,46)(44,45)(47,50), (2,8,9)(3,6,15)(4,5,16)(10,21,29)(11,30,27)(12,33,28)(13,17,24)(14,18,23)(19,25,31)(20,26,32)(34,38,36)(35,39,37)(41,43,42)(44,47,45)(46,48,49)(50,51,52), (1,3,7,4)(2,10)(5,16,6,15)(8,17,21,18)(9,23,29,24)(11,12)(13,14)(19,33,20,30)(22,34,40,35)(25,27,26,28)(31,32)(36,38,37,39)(42,45)(43,47)(46,50)(48,51), (1,5,7,6)(2,10)(3,15,4,16)(8,19,21,20)(9,25,29,26)(11,12)(13,14)(17,30,18,33)(22,36,40,37)(23,28,24,27)(31,32)(34,39,35,38)(41,44)(42,45)(43,47)(49,52), (1,7)(2,11,10,12)(3,4)(5,6)(8,17,21,18)(9,25,29,26)(13,32,14,31)(15,16)(19,33,20,30)(22,38,40,39)(23,28,24,27)(34,36,35,37)(41,44)(43,47)(46,50)(48,51), (1,7)(2,13,10,14)(3,4)(5,6)(8,19,21,20)(9,27,29,28)(11,31,12,32)(15,16)(17,30,18,33)(22,34,40,35)(23,25,24,26)(36,38,37,39)(41,44)(42,45)(46,50)(49,52), (41,44)(42,45)(43,47)(46,50)(48,51)(49,52), (1,7)(3,4)(5,6)(8,21)(9,29)(15,16)(17,18)(19,20)(22,40)(23,24)(25,26)(27,28)(30,33)(34,35)(36,37)(38,39), (1,7)(2,10)(3,4)(5,6)(9,29)(11,12)(13,14)(15,16)(22,40)(23,24)(25,26)(27,28)(31,32)(34,35)(36,37)(38,39), (1,7)(2,10)(3,4)(5,6)(8,21)(11,12)(13,14)(15,16)(17,18)(19,20)(22,40)(30,33)(31,32)(34,35)(36,37)(38,39), (2,10)(8,21)(9,29)(11,12)(13,14)(17,18)(19,20)(22,40)(23,24)(25,26)(27,28)(30,33)(31,32)(34,35)(36,37)(38,39));