Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×#14524194 |
| unambiguous semidirect product | D541⋊(C23×C4) |
| Fitting, socle | C24×C541 ⋊ C4 |
| derived, Sylow | C541 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #14524194 |
| commutator, hypocenter | C541 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C24×C541 | C4 |
| prime radical | C24×D541 | C2 |
| cosocle | D541 | C25 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C24 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
2224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1630);