Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#16864520 |
| derived, Sylow | C541 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #14524194 |
| commutator, hypocenter | C541 | C82 |
| Frattini | C2×C4 | C2×#14524194 |
| Fitting | C2×C8×C541 | C4 |
| socle, prime radical | C22×C541 | C42 |
| cosocle | C4×Dic541 | C22 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2×C8 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34624 |
2224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1389);