Finite Group DatabasebetaFinite Group Databasebeta| order | 40320 |
| isoclinism | isoclinic class of #72227517 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, socle | C24 ⋊ A7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| Fitting, socle, cosocle | C24 | A7 |
| LCS | G | |
| UCS | C1 | |
189 conjugacy classes of subgroups; only the 3 normal subgroups are shown.
This group has 189 conjugacy classes of subgroups — too many to draw. Only its 3 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 16 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,6)(3,4,7,15)(5,9,10,16)(8,12,11,14);(1,5,15,10,11,12,13,9,2,3,6,7,8,16)(4,14)15 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,6)(3,4,7,15)(5,9,10,16)(8,12,11,14), (1,5,15,10,11,12,13,9,2,3,6,7,8,16)(4,14));