Finite Group DatabasebetaFinite Group Databasebeta| order | 4508 |
| automorphism | Aut(G) order 2082696 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1127 |
| unambiguous semidirect product | C23⋊Dic49 |
| unambiguous semidirect product | C49⋊Dic23 |
| derived, Hall | C23×C49 ⋊ C4 |
| Sylow | C49 ⋊ Dic23 |
| Sylow | C23 ⋊ Dic49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1127 |
| commutator, hypocenter | C23×C49 | C4 |
| Frattini | C2×C7 | D161 |
| Fitting, cosocle | C2×C23×C49 | C2 |
| socle, prime radical | C2×C7×C23 | D7 |
| LCS | G ▷ C23×C49 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 76 |
| transitive degree | μt(G) = 4508 |
Polycyclic presentation:
2,7,23,2,7|a^2=d,b^7=e^6,b^a=b^6e,c^a=c^22,e^a=e^61130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23⋊((C49⋊C3)⋊C4), C3×Dic1127, Dic3381, … |
| maximal normal subgroup of | C23⋊((C49⋊C3)⋊C4), C3×Dic1127, C5×Dic1127, … |
| maximal quotient of | C3×Dic1127, Dic3381, C5×Dic1127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4508, 4);