Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C2×D3×#120 (order 384) · Inn(G) = C2×D3 · Out(G) = C22×D4 |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2,3)(5,7);(2,3)(4,5)(6,7)(8,9,10,12,11,13,14,15)Polycyclic presentation:
2^5,3|a^2=c,c^2=e,b^a=bd,f^a=f^236 conjugacy classes — view the full character table.
| maximal subgroup of | #4451, #4452, #4468, … |
| maximal normal subgroup of | #4451, #4452, #4468, … |
| maximal quotient of | #4524, #4525, #4528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 37);