Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C13⋊#10624391 |
| unambiguous semidirect product | (C2×C13)⋊#10624391 |
| Fitting, socle | C2×C112×C13 ⋊ D3 |
| derived, Hall | C13×C112⋊C3 ⋊ C22 |
| Hall | C112×C13 ⋊ C2×D3 |
| Hall | C112⋊C3 ⋊ C2×D13 |
| Sylow | C112 ⋊ C2×D39 |
| Sylow | C13 ⋊ C2×#10624391 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C13⋊#10624391 |
| commutator, cosocle, hypocenter | C13×C112⋊C3 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C112×C13 | D3 |
| LCS | G ▷ C13×C112⋊C3 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 858 |
592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 108);