Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C3×#383 ⋊ C2 |
| Sylow | C3 ⋊ #1521 |
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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)(4,7,8,16)(5,10,11,19)(6,13,14,15)(9,17,12,18)(21,26)(22,29)(27,31)(30,32);(2,3)(4,6)(5,9)(7,15)(8,14)(10,18)(11,12)(13,16)(17,19)(20,22)(21,25)(23,32)(24,29)(26,34)(27,35)(28,31)(30,33);(4,5)(6,12,14,9)(7,10)(8,11)(13,18,15,17)(16,19)(20,21)(22,28)(23,31)(24,26)(25,30)(27,33)(29,35)(32,34)Polycyclic presentation:
2^7,3|a^2=e,c^2=fg,d^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,d^b=dg,e^b=efg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10687595, #10687596, #10687602, … |
| maximal normal subgroup of | #10687595, #10687596, #10687602, … |
| maximal quotient of | #10683210, #10683215, #10683230, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2141);