Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C22×C4×D3 (order 96) · Inn(G) = C2×D3 · Out(G) = C2×C4 |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×C16 ⋊ C2 |
| Sylow | C3 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×D3 |
| commutator, socle | C2×C3 | C2×C8 |
| Fitting | C3×C16 | C2 |
| prime radical | C2×D3 | C8 |
| cosocle | C3×C8 | C22 |
| hypercenter | C16 | D3 |
| hypocenter | C3 | M32 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C8 ◁ C16 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,5,6,10,7,11,12,17,8,9,13,15,14,16,18,19);(2,3)(5,9)(10,15)(11,16)(17,19)Polycyclic presentation:
2^5,3|b^2=c,c^2=d,d^2=e,b^a=be,f^a=f^236 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#798, #4901, D3×M32, … |
| maximal normal subgroup of | C2×#798, #4901, D3×M32, … |
| maximal quotient of | Dic3⋊C16, #4502, (C2×D3)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 5);