Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #157⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#157⋊D3 |
| Fitting, socle | C2×C33 ⋊ D4 |
| Sylow | C33 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #157⋊D3 |
| commutator, cosocle | C3×C3⋊D3 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33 | D4 |
| hypocenter | C33 | C2×D4 |
| LCS | G ▷ C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C2 | |
192 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 11 points:
(3,4,5)(6,10)(7,8,11,9);(4,5)(7,10);(1,2)30 conjugacy classes — view the full character table.
| maximal subgroup of | #11724101, #11724104, #11724111, … |
| maximal normal subgroup of | #11724101, #11724104, #11724111, … |
| maximal quotient of | #11724333, #11724334, #11724335, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 756);