Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = C22×D3×#3003 (order 3072) · Inn(G) = D3×D4 · Out(G) = C23×D4 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#107 ⋊ C2 |
| Sylow | C3 ⋊ #467 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(4,5,6,7)(9,14)(10,16)(12,19)(13,20)(17,18)(21,23);(8,10,12,18,11,17,19,16)(9,13,15,20,14,21,22,23);(2,3)(5,7)(8,9)(10,13)(11,14)(12,15)(16,23)(17,21)(18,20)(19,22)Polycyclic presentation:
2^6,3|b^2=e,c^2=df,e^2=f,c^a=cd,g^a=g^2,c^b=ce,e^c=ef36 conjugacy classes — view the full character table.
| maximal subgroup of | #69193, #69194, #69196, … |
| maximal normal subgroup of | #69193, #69194, #69196, … |
| maximal quotient of | #68577, #68579, #68581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 446);