Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of D48 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #1373 |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3)(4,6,18,33,9,21,25,35,10,22,8,20,24,34,7,19)(5,11,23,31,14,27,13,26,16,29,30,32,15,28,12,17);(2,3)(4,5,8,13,9,15,7,23,10,16,18,12,24,14,25,30)(6,17,20,27,21,32,19,11,22,26,33,28,34,31,35,29)Polycyclic presentation:
2^7,3|a^2=d,b^2=ce,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2108 conjugacy classes — view the full character table.
| maximal subgroup of | #10682649, #10682650, #10682652, … |
| maximal normal subgroup of | #10682649, #10682650, #10682652, … |
| maximal quotient of | #10681927, #10681929, #10682071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 78);