Finite Group DatabasebetaFinite Group Databasebeta| order | 33810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C7 |
| direct product | C3×C23×C5⋊(C7⋊D7) |
| unambiguous semidirect product | C5⋊(C3×C23×C7⋊D7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | C5⋊(C7⋊D7) |
| commutator, cosocle, hypocenter | C5×C72 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72×C23 | C2 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C3×C23 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16905 |
8556 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33810, 79);