Finite Group DatabasebetaFinite Group Databasebeta| order | 4508 |
| isoclinism | isoclinic class of D49 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C23×D49 |
| unambiguous semidirect product | C49⋊(C22×C23) |
| unambiguous semidirect product | (C2×C49)⋊(C2×C23) |
| Fitting | C2×C23×C49 ⋊ C2 |
| derived, Sylow | C49 ⋊ C22×C23 |
| Hall | C23×C49 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D49 |
| commutator, cosocle, hypocenter | C49 | C22×C23 |
| Frattini | C7 | C2×D7×C23 |
| Fitting | C2×C23×C49 | C2 |
| socle | C2×C7×C23 | D7 |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C23 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2254 |
1196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C23×D49⋊C3, D3×C23×D49, C2×C3×C23×D49, … |
| maximal normal subgroup of | C2×C23×D49⋊C3, C2×C3×C23×D49, C2×C5×C23×D49 |
| maximal quotient of | D3×C23×D49, C2×C3×C23×D49, C2×C23×D147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4508, 8);