Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of #213 |
| automorphism | Aut(G) = C23×D3×D4 (order 384) · Inn(G) = #67 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #103 |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2,3)(4,5,6,7)(9,12)(10,15)(13,14);(2,3)(8,9,11,14)(10,12,15,13)Polycyclic presentation:
2^5,3|a^2=e,b^2=c,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 | #4765, #4767, #4768, … |
| maximal normal subgroup of | #4765, #4767, #4768, … |
| maximal quotient of | #4452, #4481, #4484, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 17);