Finite Group DatabasebetaFinite Group Databasebeta| order | 15042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D109⋊C3 |
| unambiguous semidirect product | D109⋊(C3×C23) |
| unambiguous semidirect product | (C109⋊C3)⋊(C2×C23) |
| unambiguous semidirect product | (C23×D109)⋊C3 |
| Fitting, socle, Hall | C23×C109 ⋊ C2×C3 |
| derived, Sylow | C109 ⋊ C2×C3×C23 |
| Hall | C23×C109⋊C3 ⋊ C2 |
| Hall | C23×D109 ⋊ C3 |
| Hall | C109⋊C3 ⋊ C2×C23 |
| Hall | D109 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D109⋊C3 |
| commutator, cosocle, hypocenter | C109 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C109 | C2×C3 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2507 |
552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#89137⋊C3, C23⋊(#89137⋊C3), D23×D109⋊C3, … |
| maximal normal subgroup of | C23×#89137⋊C3, C23⋊(#89137⋊C3), D23×D109⋊C3, … |
| maximal quotient of | C23×Dic109⋊C3, C2×C23×D109⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15042, 10);