Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = D3×#2846 (order 768) · Inn(G) = C2×D3 · Out(G) = C2×#120 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D3 |
| commutator | C2×C3 | C22×C4 |
| Frattini | C22 | C22×D3 |
| Fitting | C3×C42 | C2 |
| socle, cosocle | C22×C3 | C23 |
| prime radical | C22×D3 | C22 |
| hypercenter | C42 | D3 |
| hypocenter | C3 | #117 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(4,5,6,7)(9,13)(12,15);(8,10,11,14)(9,12,13,15);(2,3)(8,9)(10,12)(11,13)(14,15)Polycyclic presentation:
2^5,3|b^2=e,c^2=d,c^a=ce,f^a=f^236 conjugacy classes — view the full character table.
| maximal subgroup of | #4689, #4690, #4708, … |
| maximal normal subgroup of | #4689, #4690, #4708, … |
| maximal quotient of | #4650, #4651, #4652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 79);