Finite Group DatabasebetaFinite Group Databasebeta| order | 15028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D221⋊D17 |
| unambiguous semidirect product | (C17⋊D17)⋊D13 |
| Fitting, socle, derived, Hall | C13×C172 ⋊ C22 |
| Sylow | C172 ⋊ C2×D13 |
| Sylow | C13 ⋊ D172 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C172 | C22 |
| LCS | G ▷ C13×C172 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 442 |
Polycyclic presentation:
2^2,13,17^2|c^a=c^12,d^a=d^16,d^b=d^16,e^b=e^16976 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15028, 45);