Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #1791 |
548 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 121 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)(5,11)(6,15)(8,19)(9,18)(10,22)(12,25)(13,24)(14,28)(16,29)(17,30)(20,32)(21,31)(23,33)(26,35)(27,34);(4,6)(5,10)(7,15)(8,20)(9,16)(11,22)(12,14)(13,27)(17,21)(18,29)(19,32)(23,26)(24,34)(25,28)(30,31)(33,35);(2,3)(4,5,8,13,9,12,21,26)(6,14,17,27,16,10,20,23)(7,11,19,24,18,25,31,35)(15,22,30,33,29,28,32,34)Polycyclic presentation:
2^7,3|a^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,e^b=eg,f^b=fg,d^c=dg66 conjugacy classes — view the full character table.
| maximal subgroup of | #10712477, #10712478, #10712484, … |
| maximal normal subgroup of | #10712477, #10712478, #10712484, … |
| maximal quotient of | #10686580, #10686583, #10686708, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4721);