Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1328 |
90 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)(5,10,11,21)(7,15)(8,16)(9,14)(12,25,23,20)(13,22,24,32)(17,27)(18,29)(19,28)(26,34,33,31)(30,35);(1,2,3)(4,5,7,12,8,13,18,26,9,11,17,23,19,24,30,33)(6,10,15,20,16,22,29,31,14,21,27,25,28,32,35,34)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=cg,d^b=de,h^b=h^2,d^c=dg48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1328, C2×#67533, #10704379, … |
| maximal normal subgroup of | D3×#1328, C2×#67533, #10704379, … |
| maximal quotient of | #10681825, #10681827, #10681828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 109);