Finite Group DatabasebetaFinite Group Databasebeta| order | 11520 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| derived | #72209614 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #72209614 | C2 |
| Frattini, Fitting, socle | C24 | S6 |
| LCS | G ▷ #72209614 | |
| UCS | C1 | |
455 conjugacy classes of subgroups; only the 4 normal subgroups are shown.
This group has 455 conjugacy classes of subgroups — too many to draw. Only its 4 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Permutation generators:
(3,32,26)(4,9,31)(8,33,25)(10,23,18)(11,20,17)(12,15,14)(16,21,24)(27,30,29);(3,26,17)(4,16,9)(8,25,18)(10,33,23)(11,32,20)(12,29,30)(14,15,27)(21,31,24);(2,12,15)(3,25,18)(4,28,31)(8,26,17)(10,33,20)(11,32,23)(13,16,21)(19,27,30);(1,12,16)(2,32,28)(4,15,8)(7,27,31)(9,14,10)(13,19,17)(21,30,23)(24,29,25);(4,16,21,31)(10,33,25,18)(11,32,26,17)(12,15,27,30)21 conjugacy classes — view the full character table.
| maximal subgroup of | #72218858, C2×#72218848 |
| maximal normal subgroup of | #72218858, C2×#72218848 |
| maximal quotient of | C2×#72218848 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:
gap> G := Group((3,32,26)(4,9,31)(8,33,25)(10,23,18)(11,20,17)(12,15,14)(16,21,24)(27,30,29), (3,26,17)(4,16,9)(8,25,18)(10,33,23)(11,32,20)(12,29,30)(14,15,27)(21,31,24), (2,12,15)(3,25,18)(4,28,31)(8,26,17)(10,33,20)(11,32,23)(13,16,21)(19,27,30), (1,12,16)(2,32,28)(4,15,8)(7,27,31)(9,14,10)(13,19,17)(21,30,23)(24,29,25), (4,16,21,31)(10,33,25,18)(11,32,26,17)(12,15,27,30));