Finite Group DatabasebetaFinite Group Databasebeta| order | 26176 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D409 |
| unambiguous semidirect product | C409⋊C26 |
| unambiguous semidirect product | (C2×C409)⋊C25 |
| Fitting, socle | C25×C409 ⋊ C2 |
| derived, Sylow | C409 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D409 |
| commutator, cosocle, hypocenter | C409 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C409 | C2 |
| LCS | G ▷ C409 | |
| UCS | C1 ◁ C25 | |
5650 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13088 |
6592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26176, 1387);