Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#333 ⋊ C2 |
| Sylow | C3 ⋊ #1554 |
198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2)(4,7,9,8)(5,11,12,16)(6,14,15,17)(10,18,13,19)(21,26)(25,34)(27,31)(28,35);(2,3)(4,6,9,15)(5,10,12,13)(7,14,8,17)(11,18,16,19)(20,22,24,30)(21,25,26,34)(23,32,33,29)(27,35,31,28);(4,5,8,11,9,12,7,16)(6,13,14,18,15,10,17,19)(20,21)(22,28)(23,31)(24,26)(25,29)(27,33)(30,35)(32,34)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=fg,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,d^b=dg,e^b=efg,h^b=h^2,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1554, C2×#68486, #10763572, … |
| maximal normal subgroup of | D3×#1554, C2×#68486, #10763572, … |
| maximal quotient of | #10683213, #10683223, #10683337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1062);