Finite Group DatabasebetaFinite Group Databasebeta| order | 33810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C5⋊#64418 |
| unambiguous semidirect product | C5⋊(C23×#64418) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C5⋊#64418 |
| commutator, cosocle, hypocenter | C5×#3862 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C23 | D3 |
| LCS | G ▷ C5×#3862 | |
| UCS | C1 ◁ C23 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1610 |
1334 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33810, 45);