Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| automorphism | Aut(G) = D3×D42 (order 384) · Inn(G) = C2×#67 · Out(G) = C23 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×Q8 ⋊ C2 |
| Sylow | C3 ⋊ #137 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(4,7,9,16)(5,11,12,19)(6,13,8,15)(10,18,17,14);(4,6,9,8)(5,10,12,17)(7,15,16,13)(11,14,19,18);(2,3)(4,5)(6,10)(7,14)(8,17)(9,12)(11,13)(15,19)(16,18)Polycyclic presentation:
2^5,3|b^2=e,c^2=e,d^2=e,c^a=cd,d^a=de,f^a=f^2,c^b=ce,d^c=de21 conjugacy classes — view the full character table.
| maximal subgroup of | #4754, #4755, #5061, … |
| maximal normal subgroup of | #4754, #4755, #5061, … |
| maximal quotient of | #4964, #4966, #4967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 149);