Finite Group DatabasebetaFinite Group Databasebeta| order | 4624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#72213364 |
| Fitting, socle | C2×C172 ⋊ C2×C4 |
| derived, Sylow | C172 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #72213364 |
| commutator, hypocenter | C172 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C172 | C2×C4 |
| prime radical | C2×D172 | C2 |
| cosocle | C17⋊D17 | C23 |
| LCS | G ▷ C172 | |
| UCS | C1 ◁ C2 | |
172 conjugacy classes of subgroups.
112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72213374, #72218888, #72218891, … |
| maximal normal subgroup of | C2×#72213374, #72218888, #72218891 |
| maximal quotient of | #72218888, D3×#72213364 |
Past the SmallGroups library coverage — no SmallGroups id.