Finite Group DatabasebetaFinite Group Databasebeta| order | 33810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C7×C23×D105 |
| unambiguous semidirect product | C3⋊(C7×C23×D35) |
| unambiguous semidirect product | C5⋊(C7×C23×D21) |
| unambiguous semidirect product | C7⋊(C7×C23×D15) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C23 | D105 |
| commutator, cosocle, hypocenter | C3×C5×C7 | C2×C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C23 | C2 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C7×C23 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4830 |
8694 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33810, 89);