Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,14)(12,15)(16,22)(17,20)(18,21)(19,23)(24,25,30,35)(26,36,39,49)(27,32,41,47)(28,34,29,33)(31,43,45,38)(37,50,53,54)(40,48,42,46)(44,51,55,52);(8,10)(9,13)(11,16)(12,17)(14,19)(15,20)(18,23)(21,22)(24,26)(25,31)(27,37)(28,38)(29,43)(30,39)(32,44)(33,36)(34,49)(35,45)(40,51)(41,53)(42,52)(46,54)(47,55)(48,50);(8,11)(9,14)(10,16)(12,18)(13,19)(15,21)(17,23)(20,22)(24,27,30,41)(25,32,35,47)(26,37,39,53)(28,42,29,40)(31,44,45,55)(33,48,34,46)(36,50,49,54)(38,52,43,51);(9,15)(13,20)(14,21)(19,22)(24,28,30,29)(25,33,35,34)(26,38,39,43)(27,40,41,42)(31,36,45,49)(32,46,47,48)(37,51,53,52)(44,54,55,50)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11443);