Finite Group DatabasebetaFinite Group Databasebeta| order | 17710 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | D35×C23⋊C11 |
| unambiguous semidirect product | C5⋊(D7×C23⋊C11) |
| unambiguous semidirect product | C7⋊(D5×C23⋊C11) |
| unambiguous semidirect product | (C23×D35)⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C23 | C2×C11 |
| LCS | G ▷ C5×C7×C23 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 805 |
247 conjugacy classes — view the full character table.
| maximal subgroup of | D35×AGL(1,𝔽23), D35⋊AGL(1,𝔽23), D5×D7×C23⋊C11, … |
| maximal normal subgroup of | D35×AGL(1,𝔽23), D35⋊AGL(1,𝔽23), D5×D7×C23⋊C11, … |
| maximal quotient of | Dic35×C23⋊C11, C2×D35×C23⋊C11 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17710, 24);