Finite Group DatabasebetaFinite Group Databasebeta| order | 18676 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(C23⋊#1181) |
| unambiguous semidirect product | C23⋊(C7⋊#1181) |
| Fitting, socle, derived, Hall | C7×C23×C29 ⋊ C4 |
| Hall | C23×C29 ⋊ Dic7 |
| Hall | C7×C29 ⋊ Dic23 |
| Hall | C7×C23 ⋊ #1181 |
| Sylow | C29 ⋊ Dic161 |
| Sylow | C23 ⋊ C7⋊#1181 |
| Sylow | C7 ⋊ C23⋊#1181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C23×C29 | C4 |
| prime radical, cosocle | C7×C23×D29 | C2 |
| LCS | G ▷ C7×C23×C29 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4669 |
Polycyclic presentation:
2^2,7,23,29|a^2=b,c^a=c^6,d^a=d^22,e^a=e^17,e^b=e^281291 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18676, 26);