Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C25×D3×D4 (order 1536) · Inn(G) = C2×D12 · Out(G) = C25 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #485 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,3)(5,9)(6,10)(12,15,16,23,17,24,14,21)(13,19,18,22,20,26,25,27);(4,6)(5,8)(7,10)(9,11)(12,14,17,16)(13,18,20,25)(15,21,24,23)(19,22,26,27);(2,3)(4,5,7,9)(6,8,10,11)(12,13)(14,18)(15,22)(16,25)(17,20)(19,23)(21,26)(24,27)Polycyclic presentation:
2^6,3|a^2=e,b^2=f,c^2=de,d^2=f,c^a=cd,d^a=df,g^a=g^2,c^b=ce39 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#4723, #78591, #78614, … |
| maximal normal subgroup of | C2×#4723, #78591, #78614, … |
| maximal quotient of | #68621, #68622, #68627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 282);