Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#349 ⋊ C2 |
| Sylow | C3 ⋊ #2191 |
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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:
(1,2,3)(7,20)(11,30)(14,32)(15,25)(18,34)(19,35)(22,28)(29,33);(2,3)(4,6)(5,10)(7,19)(8,24)(9,16)(11,29)(12,31)(13,26)(14,18)(15,22)(17,21)(20,35)(23,27)(25,28)(30,33)(32,34);(2,3)(4,5,9,13)(6,14,16,32)(7,18,20,34)(8,23,21,12)(10,25,26,15)(11,28,30,22)(17,33,24,29)(19,31,35,27)Polycyclic presentation:
2^7,3|a^2=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^2,d^b=df,e^b=eg,f^b=fg,h^b=h^2,d^c=dg42 conjugacy classes — view the full character table.
| maximal subgroup of | #10707358, #10707359, #10707364, … |
| maximal normal subgroup of | #10707358, #10707359, #10707364, … |
| maximal quotient of | #10707303, #10707308, #10707314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1697);