Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | C7⋊#16809854 |
| derived, Hall | C7×C292 ⋊ C4 |
| Sylow | C292 ⋊ Dic7 |
| Sylow | C7 ⋊ #16809854 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(C29⋊D29) |
| commutator, hypocenter | C7×C292 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C7×C292 | C2 |
| LCS | G ▷ C7×C292 | |
| UCS | C1 ◁ C2 | |
192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23548 |
Polycyclic presentation:
2,7,29^2,2|a^2=e,b^a=b^6,c^a=c^28,d^a=d^285890 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 41);