Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#31772625 |
| Fitting | C2×C42×C541 ⋊ C2 |
| Sylow | C541 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D541 |
| commutator, cosocle | C22×C541 | C24 |
| Frattini | C22 | C23×D541 |
| Fitting | C2×C42×C541 | C2 |
| socle | C23×C541 | C23 |
| hypercenter | C2×C42 | D541 |
| hypocenter | C541 | C2×#127 |
| LCS | G ▷ C22×C541 ▷ C541 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17312 |
8668 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1089);