Finite Group DatabasebetaFinite Group Databasebeta| order | 26868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C2239 ⋊ C2×C3 |
| derived, Sylow | C2239 ⋊ C22×C3 |
| Hall | C2×D2239 ⋊ C3 |
| Hall | C2239⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2239⋊C3 |
| commutator, cosocle, hypocenter | C2239 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C2239 | C2×C3 |
| LCS | G ▷ C2239 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4478 |
758 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26868, 8);