Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#347 ⋊ C2 |
| Sylow | C3 ⋊ #2110 |
160 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 85 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:
(2,3)(6,15)(10,23)(14,29)(16,18)(17,31)(22,32)(24,25)(30,33);(1,2,3)(4,6)(5,10,12,23)(7,18)(8,17)(9,15)(11,25,26,24)(13,14,28,29)(16,20)(19,22)(21,31)(27,33,35,30)(32,34);(4,5,7,11,8,13,19,27,9,12,20,26,21,28,34,35)(6,14,16,30,17,23,32,25,15,29,18,33,31,10,22,24)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,c^b=cg,d^b=dg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10706366, #10706368, #10706371, … |
| maximal normal subgroup of | #10706366, #10706368, #10706371, … |
| maximal quotient of | #10704190, #10704194, #10704228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1663);