Finite Group DatabasebetaFinite Group Databasebeta| order | 5832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23 |
| direct product | D33×3−1+2 |
| Fitting, Sylow | C33×3−1+2 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×D33 |
| commutator, socle, cosocle | C34 | C23×C32 |
| Fitting | C33×3−1+2 | C23 |
| prime radical | C32×D33 | C3 |
| hypercenter | 3−1+2 | D33 |
| hypocenter | C33 | C23×3−1+2 |
| LCS | G ▷ C34 ▷ C33 | |
| UCS | C1 ◁ C3 ◁ 3−1+2 | |
2737 conjugacy classes of subgroups; only the 266 normal subgroups are shown.
This group has 2737 conjugacy classes of subgroups — too many to draw. Only its 266 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,3)(4,5,6)(7,8)(10,16,17,15,13,14,12,11,18);(1,2,3)(5,6)(11,13,16)(14,18,17);(8,9)297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D32×#92265 |
| maximal quotient of | D32×#92265 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((2,3)(4,5,6)(7,8)(10,16,17,15,13,14,12,11,18), (1,2,3)(5,6)(11,13,16)(14,18,17), (8,9));