Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4×D541 |
| Fitting | C23×C4×C541 ⋊ C2 |
| derived, Sylow | C541 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D541 |
| commutator, hypocenter | C541 | C24×C4 |
| Frattini | C2 | C24×D541 |
| Fitting | C23×C4×C541 | C2 |
| socle | C24×C541 | C22 |
| prime radical | C24×D541 | C2 |
| cosocle | C2×C541 | C25 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C23×C4 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17312 |
8704 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1367);