Finite Group DatabasebetaFinite Group Databasebeta| order | 15246 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C112 · Schur multiplier (H2) = C3×C11 |
| direct product | C32×C112×D7 |
| Fitting, socle, Hall | C32×C7×C112 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C32×C112 |
| Hall | C7×C112 ⋊ C2×C32 |
| Hall | C32×C7 ⋊ C2×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C112 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C32×C112 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C112 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C32×C112 | |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7623 |
5445 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C11×D7×D11, C32×D7×C11⋊D11, C3×D3×C112×D7, … |
| maximal normal subgroup of | C32×C11×D7×D11, C32×D7×C11⋊D11, C3×D3×C112×D7, … |
| maximal quotient of | C32×C112×Dic7, C2×C32×C112×D7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15246, 114);