Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of #213 |
| automorphism | Aut(G) = C22×D3×D4 (order 192) · Inn(G) = #67 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #104 |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 11 points:
(1,2,3)(4,6)(5,8)(7,10)(9,11);(2,3)(4,5,7,9,8,6,11,10)Polycyclic presentation:
2^5,3|a^2=c,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,d^b=de24 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#104, #4821, #5144, … |
| maximal normal subgroup of | D3×#104, #4821, #5144, … |
| maximal quotient of | #4532, D4⋊(C3⋊C8), #4535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 44);