Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C7 |
| direct product | H(5,𝔽2)×#3862 |
| Fitting, Hall | C72×H(5,𝔽2) ⋊ C3 |
| Sylow | C72 ⋊ C3×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×#3862 |
| commutator, socle, cosocle | C2×C72 | C24×C3 |
| Fitting | C72×H(5,𝔽2) | C3 |
| hypercenter | H(5,𝔽2) | #3862 |
| hypocenter | C72 | C3×H(5,𝔽2) |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
830 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
323 conjugacy classes. The character table is too large to display.
| maximal subgroup of | H(5,𝔽2)×#64425, B(4,𝔽2)×#3862, #72246203, … |
| maximal normal subgroup of | H(5,𝔽2)×#64425, B(4,𝔽2)×#3862, #72246203, … |
Past the SmallGroups library coverage — no SmallGroups id.