Finite Group DatabasebetaFinite Group Databasebeta| order | 3136 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#13096696 |
| Fitting | C2×C72×D4 ⋊ C22 |
| Sylow | C72 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D72 |
| commutator, cosocle | C2×C72 | C25 |
| Frattini | C2 | C23×D72 |
| Fitting | C2×C72×D4 | C22 |
| socle | C22×C72 | C24 |
| hypercenter | C2×D4 | D72 |
| hypocenter | C72 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
2150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
244 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72214319, C2×#72214244 |
| maximal normal subgroup of | C2×#72214319, C2×#72214244 |
Past the SmallGroups library coverage — no SmallGroups id.