Finite Group DatabasebetaFinite Group Databasebeta| order | 15916 |
| isoclinism | isoclinic class of D173 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C2×C23×D173 |
| unambiguous semidirect product | C173⋊(C22×C23) |
| unambiguous semidirect product | (C2×C173)⋊(C2×C23) |
| Fitting, socle | C2×C23×C173 ⋊ C2 |
| derived, Sylow | C173 ⋊ C22×C23 |
| Hall | C23×C173 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | D173 |
| commutator, cosocle, hypocenter | C173 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C173 | C2 |
| LCS | G ▷ C173 | |
| UCS | C1 ◁ C2×C23 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7958 |
4048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15916, 11);