Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C4×D8 ⋊ C2 |
| Sylow | C3 ⋊ #3169 |
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(4,6,7,10)(5,9,8,11);(12,13,17,19,15,18,14,16);(2,3)(5,8)(9,11);(4,5)(6,9)(7,8)(10,11)(13,16)(14,17)(18,19)Polycyclic presentation:
2^7,3|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10705160, #10705178, #10705191, … |
| maximal normal subgroup of | #10705160, #10705178, #10705191, … |
| maximal quotient of | #10795723, #10799403, #10799405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12174);