Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C4×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2392 |
696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(12,14,15,18)(13,17,16,19);(2,3)(5,7)(9,11);(2,3)(8,9)(10,11)(13,16)(17,19);(4,5,6,7)(12,13)(14,17)(15,16)(18,19)Polycyclic presentation:
2^7,3|a^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^2,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10690285, #10690290, #10767458, … |
| maximal normal subgroup of | #10690285, #10690290, #10767458, … |
| maximal quotient of | #10716867, #10716886, #10716926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6352);