Finite Group DatabasebetaFinite Group Databasebeta| order | 26100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D725 |
| unambiguous semidirect product | (C2×C25)⋊(C32×D29) |
| unambiguous semidirect product | (C2×C29)⋊(C32×D25) |
| Fitting | C2×C32×C25×C29 ⋊ C2 |
| derived, Hall | C25×C29 ⋊ C22×C32 |
| Hall | C32×C25×C29 ⋊ C22 |
| Hall | C32×C29 ⋊ C2×D25 |
| Hall | C32×C25 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C32×D25 |
| Sylow | C25 ⋊ C2×C32×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D725 |
| commutator, cosocle, hypocenter | C25×C29 | C22×C32 |
| Frattini | C5 | C2×C32×D145 |
| Fitting | C2×C32×C25×C29 | C2 |
| socle | C2×C32×C5×C29 | D5 |
| LCS | G ▷ C25×C29 | |
| UCS | C1 ◁ C2×C32 | |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13050 |
6552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26100, 128);