Finite Group DatabasebetaFinite Group Databasebeta| order | 15548 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#10621728 |
| Fitting, socle, derived, Hall | C132×C23 ⋊ C4 |
| Sylow | C132 ⋊ Dic23 |
| Sylow | C23 ⋊ #10621728 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132×C23 | C4 |
| prime radical, cosocle | C23×C13⋊D13 | C2 |
| LCS | G ▷ C132×C23 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3887 |
Polycyclic presentation:
2^2,13^2,23|a^2=b,c^a=c^5,d^a=d^5,e^a=e^22,c^b=c^12,d^b=d^12992 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15548, 23);