Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1358 |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(2,3)(4,6,9,18)(5,10,14,26)(7,19,21,33)(8,22,23,17)(11,25,13,15)(12,28,30,32)(16,20,34,31)(24,27,35,29);(1,2,3)(4,5,7,12,8,11,20,27,9,14,21,30,23,13,31,29)(6,15,16,32,17,26,33,35,18,25,34,28,22,10,19,24)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,c^2=f,d^2=ef,e^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,c^b=cf,d^b=defg,e^b=eg,h^b=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1358, C2×#67572, #10706395, … |
| maximal normal subgroup of | D3×#1358, C2×#67572, #10706395, … |
| maximal quotient of | #10681909, #10681919, #10681921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 148);