Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #1483 |
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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 — 3 generators on 19 points:
(1,2,3)(5,9)(8,11);(2,3)(4,5)(6,11)(7,9)(8,10)(12,14)(13,16)(15,17)(18,19);(5,8)(6,10)(9,11)(12,13,15,18,16,14,19,17)Polycyclic presentation:
2^7,3|a^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cfg,d^b=df,h^b=h^278 conjugacy classes — view the full character table.
| maximal subgroup of | #10686979, #10686981, #10686984, … |
| maximal normal subgroup of | #10686979, #10686981, #10686984, … |
| maximal quotient of | #10683619, #10683624, #10683629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3003);