Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1342 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2)(4,6,10,19)(5,11,14,28)(7,21,24,33)(8,18,9,17)(12,29,31,35)(13,26,25,27)(15,30,32,20)(16,23,34,22);(2,3)(4,5,8,13,10,14,9,25)(6,15,17,29,19,32,18,35)(7,20,22,12,24,30,23,31)(11,21,26,34,28,33,27,16)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,c^2=fg,d^2=g,e^2=g,f^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^2,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^2,d^c=dg42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1342, C2×#67537, #10705347, … |
| maximal normal subgroup of | D3×#1342, C2×#67537, #10705347, … |
| maximal quotient of | #10681891, #10681894, #10681903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 113);