Finite Group DatabasebetaFinite Group Databasebeta| order | 144 |
| isoclinism | isoclinic class of D3 |
| automorphism | Aut(G) = C2×D3×#5934 (order 2304) · Inn(G) = D3 · Out(G) = C2×#5934 |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×Dic3 |
| derived | C3 ⋊ C22×C3×C4 |
| Sylow | C32 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | D3 |
| commutator, hypocenter | C3 | C22×C3×C4 |
| Frattini | C2 | C22×C3×D3 |
| Fitting, socle, prime radical | C23×C32 | C2 |
| cosocle | C2×C3 | C23×C3 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C23×C3 | |
124 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2)(3,4)(6,7)(8,9,10)(11,12,13,14);(3,4)(5,6,7);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #63579, C3×C3⋊#95, #63952, … |
| maximal normal subgroup of | #63579, C3×C3⋊#95, #63952, … |
| maximal quotient of | C22×C3×C3⋊C8, C2×C3×#208, C2×C3×C4×Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(144, 166);