Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | D33×C3⋊D3 |
| Fitting, socle, derived, Sylow | C35 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C35 | C24 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
6732 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 6732 conjugacy classes of subgroups — too many to draw. Only its 322 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(7,9,8)(10,11)(13,14);(5,6)(8,9)(11,12)(14,15);(2,3)(4,6,5);(11,12)162 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((1,2,3)(7,9,8)(10,11)(13,14), (5,6)(8,9)(11,12)(14,15), (2,3)(4,6,5), (11,12));