Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211 |
| direct product | C22×#11714171 |
| Fitting | C23×B(4,𝔽2) ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#1020⋊C2 |
| commutator, cosocle, hypocenter | #997 | C25 |
| Frattini | C23 | C24×S4 |
| Fitting | C23×B(4,𝔽2) | D3 |
| hypercenter | C24 | #1020⋊C2 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C23 ◁ C24 | |
33170 conjugacy classes of subgroups; only the 535 normal subgroups are shown.
This group has 33170 conjugacy classes of subgroups — too many to draw. Only its 535 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72217027 |
| maximal normal subgroup of | C22×#72217027 |
| maximal quotient of | C2×#72246216 |
Past the SmallGroups library coverage — no SmallGroups id.