Finite Group DatabasebetaFinite Group Databasebeta| order | 26588 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C17 |
| direct product | D23×C17⋊D17 |
| unambiguous semidirect product | (C17×D23)⋊D17 |
| Fitting, socle, derived, Hall | C172×C23 ⋊ C22 |
| Sylow | C172 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×C17⋊D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C172×C23 | C22 |
| LCS | G ▷ C172×C23 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6647 |
1898 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26588, 27);