Finite Group DatabasebetaFinite Group Databasebeta| order | 5832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#72221851 |
| Fitting | C2×#10624869 ⋊ C22 |
| derived, Sylow | #10624869 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #4207⋊D3 |
| commutator, cosocle, hypocenter | #10624869 | C23 |
| Frattini | C32 | C2×C3⋊#1113 |
| Fitting | C2×#10624869 | C22 |
| socle | C2×C32 | C3⋊#1113 |
| LCS | G ▷ #10624869 | |
| UCS | C1 ◁ C2×C3 | |
1734 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221857, C2×#72221868 |
| maximal normal subgroup of | C2×#72221868 |
Past the SmallGroups library coverage — no SmallGroups id.