Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C213 |
| direct product | C2×#72227619 |
| Fitting, Sylow | C2×H(9,𝔽2) ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C24×C22⋊A4 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C25×C3 |
| Frattini | C2 | C25×C22⋊A4 |
| Fitting | C2×H(9,𝔽2) | C3 |
| hypercenter | C2×H(5,𝔽2) | C22⋊A4 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
2777717 conjugacy classes of subgroups.
| transitive degree | μt(G) = 64 |
262 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72268029, #72268037, #72271526, … |
| maximal normal subgroup of | #72268037, #72271725 |
Past the SmallGroups library coverage — no SmallGroups id.