Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C3 ⋊ #1796 |
536 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 536 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)(9,20)(10,24)(12,26)(13,18)(14,28)(16,30)(17,31)(21,33)(22,34)(23,35)(25,32)(27,29);(4,6,9,17)(5,10,13,25)(7,15,20,31)(8,22,23,16)(11,24,18,32)(12,27,21,14)(19,34,35,30)(26,29,33,28);(2,3)(4,5)(6,14)(7,18,20,11)(8,21)(9,13)(10,16)(12,23)(15,29,31,28)(17,27)(19,26,35,33)(22,25)(24,30,32,34)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,d^b=dg,f^c=fg63 conjugacy classes — view the full character table.
| maximal subgroup of | #10710737, #10710739, #10710747, … |
| maximal normal subgroup of | #10710737, #10710739, #10710747, … |
| maximal quotient of | #10686609, #10686613, #10686618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4720);