Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×C4×M16 ⋊ C2 |
| Sylow | C3 ⋊ #2920 |
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(13,16)(17,19);(4,6,7,10)(5,9,8,11);(2,3)(5,8)(9,11);(4,5)(6,9)(7,8)(10,11)(12,13,14,17,15,16,18,19)Polycyclic presentation:
2^7,3|a^2=f,c^2=e,f^2=g,b^a=be,d^a=dg,h^b=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | #10684685, #10684689, #10684693, … |
| maximal normal subgroup of | #10684685, #10684689, #10684693, … |
| maximal quotient of | #10792662, C4×#5126, C4×#5118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11093);