Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C22⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #2974 |
464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(5,9)(8,10)(13,16)(17,19);(6,11)(8,10);(2,3)(4,6)(5,8)(7,11)(9,10)(13,16)(17,19);(4,5)(6,10)(7,9)(8,11)(12,13,15,17,14,16,18,19)Polycyclic presentation:
2^7,3|a^2=f,f^2=g,b^a=be,d^a=de,c^b=ceg,h^b=h^290 conjugacy classes — view the full character table.
| maximal subgroup of | #10761447, #10761450, #10761456, … |
| maximal normal subgroup of | #10761447, #10761450, #10761456, … |
| maximal quotient of | #10793867, #10793869, #10793925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11179);