Finite Group DatabasebetaFinite Group Databasebeta| order | 18170 |
| isoclinism | isoclinic class of D115 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×D115 |
| unambiguous semidirect product | C5⋊(D23×C79) |
| unambiguous semidirect product | C23⋊(D5×C79) |
| Fitting, socle, Hall | C5×C23×C79 ⋊ C2 |
| derived, Hall | C5×C23 ⋊ C2×C79 |
| Hall | C23×C79 ⋊ D5 |
| Hall | C5×C79 ⋊ D23 |
| Sylow | C23 ⋊ D5×C79 |
| Sylow | C5 ⋊ D23×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | D115 |
| commutator, cosocle, hypocenter | C5×C23 | C2×C79 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C79 | C2 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C79 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9085 |
4661 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D79×D115, D5×D23×C79, D115⋊D79, … |
| maximal normal subgroup of | D79×D115, D5×D23×C79, D115⋊D79, … |
| maximal quotient of | C79×Dic115, C2×C79×D115 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18170, 7);