Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×H(3,ℤ/4) ⋊ C2 |
| Sylow | C3 ⋊ #2053 |
264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2)(4,7,8,22,10,24,9,23)(5,12,13,20,14,30,25,33)(6,16,17,31,19,32,18,21)(11,26,15,29,28,35,27,34);(2,3)(4,6)(5,11)(7,21)(8,18)(9,17)(10,19)(12,29)(13,27)(14,28)(15,25)(16,23)(20,26)(22,32)(24,31)(30,34)(33,35);(2,3)(4,5)(6,15)(7,20)(8,25)(9,13)(10,14)(11,17)(12,22)(16,26)(18,28)(19,27)(21,29)(23,30)(24,33)(31,34)(32,35)Polycyclic presentation:
2^7,3|c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,c^b=cf,d^b=dg,f^b=fg,h^b=h^2,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10707697, #10707702, #10707708, … |
| maximal normal subgroup of | #10707697, #10707702, #10707708, … |
| maximal quotient of | #10698924, #10698931, #10698938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1274);