Finite Group DatabasebetaFinite Group Databasebeta| order | 192 |
| isoclinism | isoclinic class of #5386 |
| automorphism | Aut(G) = C24×S4 (order 384) · Inn(G) = C2×S4 · Out(G) = C23 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4×Q8 ⋊ D3 |
73 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,4)(5,8,15)(6,17,19,10,11,20)(7,13,16)(12,18);(2,4)(5,6)(7,10)(8,12)(9,11)(13,18)(14,17)(15,20)(16,19)Polycyclic presentation:
2^3,3,2^3|b^2=cg,e^2=g,f^2=g,b^a=bc,d^a=d^2,e^a=f,f^a=e,e^d=fg,f^d=ef,f^e=fg23 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#5395, #85329, #85330, … |
| maximal normal subgroup of | C2×#5395, #85329, #85330, … |
| maximal quotient of | #73011, #73016, #73023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(192, 954);