Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C23×D3×#120 (order 1536) · Inn(G) = C22×D3 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ C8×D4 |
134 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2,3)(5,7)(8,9,10,12,11,13,14,15);(4,5,6,7);(2,3)(5,7)Polycyclic presentation:
2^6,3|b^2=e,c^2=d,d^2=f,b^a=be,g^a=g^2,c^b=ce60 conjugacy classes — view the full character table.
| maximal subgroup of | #68148, #68151, #68153, … |
| maximal normal subgroup of | #68148, #68151, #68153, … |
| maximal quotient of | #68516, #68517, #68518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 393);