Finite Group DatabasebetaFinite Group Databasebeta| order | 2880 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#10624296 |
| commutator, socle, prime radical, cosocle | C2×A6 | C22 |
| Fitting, hypercenter | C4 | #10624296 |
| hypocenter | A6 | Q8 |
| LCS | G ▷ C2×A6 ▷ A6 | |
| UCS | C1 ◁ C2 ◁ C4 | |
119 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,4,2,6)(3,7,5,8)(9,13)(10,18,17,15,16,14,12,11);(1,3,2,5)(4,8,6,7)(9,16)(10,13)(11,18)(12,17)23 conjugacy classes — view the full character table.
| maximal subgroup of | #72224456 |
| maximal normal subgroup of | #72224456 |
| maximal quotient of | #72224454 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,4,2,6)(3,7,5,8)(9,13)(10,18,17,15,16,14,12,11), (1,3,2,5)(4,8,6,7)(9,16)(10,13)(11,18)(12,17));