Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#332 ⋊ C2 |
| Sylow | C3 ⋊ #1544 |
202 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 67 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:
(2,3)(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29);(1,2,3)(4,6,8,14)(5,9,10,12)(7,15,16,13)(11,19,18,17)(20,22,25,31)(21,26,28,35)(23,30,24,33)(27,34,32,29);(4,5,7,11,8,10,16,18)(6,12,13,19,14,9,15,17)(20,21)(22,29)(23,27)(24,32)(25,28)(26,30)(31,34)(33,35)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=g,d^2=g,e^2=fg,b^a=bd,d^a=df,d^b=dg,e^b=efg,h^c=h^257 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1544, C2×#68419, #10763497, … |
| maximal normal subgroup of | D3×#1544, C2×#68419, #10763497, … |
| maximal quotient of | #10683140, #10683157, #10683486, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 995);