Finite Group DatabasebetaFinite Group Databasebeta| order | 4508 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D49 |
| unambiguous semidirect product | (C23×D49)⋊C2 |
| unambiguous semidirect product | (D23×C49)⋊C2 |
| unambiguous semidirect product | D1127⋊C2 |
| Fitting, derived, Hall | C23×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C23×C49 | C22 |
| Frattini | C7 | D7×D23 |
| socle | C7×C23 | C2×D7 |
| LCS | G ▷ C23×C49 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 72 |
| transitive degree | μt(G) = 1127 |
338 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D49⋊C3, C3×D23×D49, D23×D147, … |
| maximal normal subgroup of | D23×D49⋊C3, C3×D23×D49, C5×D23×D49 |
| maximal quotient of | C3×D23×D49, D23×D147, D49×D69, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4508, 6);