Finite Group DatabasebetaFinite Group Databasebeta| order | 26268 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C199 ⋊ C2×C3×C11 |
| derived, Sylow | C199 ⋊ C22×C3×C11 |
| Hall | C2×D199⋊C11 ⋊ C3 |
| Hall | (C199⋊C3)⋊C11 ⋊ C22 |
| Hall | C2×D199⋊C3 ⋊ C11 |
| Hall | C199⋊C11 ⋊ C22×C3 |
| Hall | C2×D199 ⋊ C3×C11 |
| Hall | C199⋊C3 ⋊ C22×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (D199⋊C3)⋊C11 |
| commutator, cosocle, hypocenter | C199 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C199 | C2×C3×C11 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 398 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26268, 20);