Finite Group DatabasebetaFinite Group Databasebeta| order | 23548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting, socle, Sylow | C292 ⋊ Dic7 |
| derived, Hall | #19154637 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | #19154637 | C4 |
| Fitting, socle | C292 | Dic7 |
| prime radical, cosocle | #26044464 | C2 |
| LCS | G ▷ #19154637 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 58 |
Polycyclic presentation:
2^2,7,29^2|a^2=b,c^a=c^6,d^a=d^13e^26,e^a=d^18e^16,d^b=d^28,e^b=e^28,d^c=d^20e^10,e^c=e^1640 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 44);