Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×Q8⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #1482 |
212 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 212 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)(6,12)(9,15)(13,18)(16,19)(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29);(2,3)(4,6)(5,9)(7,13)(8,12)(10,16)(11,15)(14,18)(17,19)(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32);(4,5,7,10,8,11,14,17)(6,9,13,16,12,15,18,19)(20,21)(22,29)(23,27)(24,32)(25,28)(26,30)(31,34)(33,35)Polycyclic presentation:
2^7,3|a^2=e,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cg,d^b=df,h^b=h^2,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1482, C2×#68233, #10761696, … |
| maximal normal subgroup of | D3×#1482, C2×#68233, #10761696, … |
| maximal quotient of | #10683528, #10683531, #10683538, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 809);