Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| automorphism | Aut(G) = D3×#72214076 (order 6144) · Inn(G) = D3×D4 · Out(G) = #2403 |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #495 |
130 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)(5,7)(9,14)(10,17)(11,20)(13,21)(16,23)(18,19);(5,7)(8,10)(9,13)(11,17)(12,19)(14,16)(15,23)(18,20)(21,22);(2,3)(4,5,6,7)(8,9)(10,16)(11,15)(12,14)(13,19)(17,21)(18,23)(20,22)Polycyclic presentation:
2^6,3|a^2=e,d^2=f,b^a=bef,c^a=cef,g^a=g^2,c^b=cd,d^b=df,d^c=df36 conjugacy classes — view the full character table.
| maximal subgroup of | #69184, #69185, #69203, … |
| maximal normal subgroup of | #69184, #69185, #69203, … |
| maximal quotient of | #70158, #70181, #70189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 714);