Finite Group DatabasebetaFinite Group Databasebeta| order | 18193 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C113⋊C7 |
| unambiguous semidirect product | C113⋊(C7×C23) |
| unambiguous semidirect product | (C23×C113)⋊C7 |
| Fitting, socle, Hall | C23×C113 ⋊ C7 |
| derived, Sylow | C113 ⋊ C7×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C113⋊C7 |
| commutator, cosocle, hypocenter | C113 | C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C113 | C7 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C23 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2599 |
529 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C23×C113⋊C7, C23×D113⋊C7, D23×C113⋊C7, … |
| maximal normal subgroup of | C2×C23×C113⋊C7, C23×D113⋊C7, D23×C113⋊C7, … |
| maximal quotient of | C2×C23×C113⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18193, 1);