Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×#101 ⋊ C2 |
| Sylow | C3 ⋊ #2133 |
230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 230 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) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3)(6,15)(10,26)(14,28)(16,19)(17,22)(25,33)(27,35)(32,34);(2,3)(4,6)(5,10)(7,19)(8,22)(9,15)(11,28)(12,27)(13,26)(14,18)(16,21)(17,24)(20,25)(23,33)(29,34)(30,32)(31,35);(4,5,8,12,9,13,24,31)(6,14,17,32,15,28,22,34)(7,18,20,30,21,11,23,29)(10,25,27,19,26,33,35,16)Polycyclic presentation:
2^7,3|a^2=e,d^2=g,e^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,d^b=dg,e^b=efg,h^b=h^2,e^d=eg45 conjugacy classes — view the full character table.
| maximal subgroup of | #10710725, #10710726, #10710728, … |
| maximal normal subgroup of | #10710725, #10710726, #10710728, … |
| maximal quotient of | #10704295, #10704347, #10704475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2704);