Finite Group DatabasebetaFinite Group Databasebeta| order | 26523 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C421 ⋊ C3×C7 |
| derived, Sylow | C421 ⋊ C32×C7 |
| Hall | C3×C421⋊C3 ⋊ C7 |
| Hall | C421⋊C7 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C421⋊C3)⋊C7 |
| commutator, cosocle, hypocenter | C421 | C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C421 | C3×C7 |
| LCS | G ▷ C421 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1263 |
123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26523, 9);