Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1812 |
260 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 105 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)(10,23)(12,25)(13,18)(14,26)(16,29)(17,30)(21,33)(22,34)(24,32)(27,28)(31,35);(4,6,8,16,9,17,22,31)(5,10,12,14,13,24,21,27)(7,15,19,29,20,30,34,35)(11,23,25,26,18,32,33,28);(2,3)(4,5)(6,14)(7,18,20,11)(8,21)(9,13)(10,16)(12,22)(15,28,30,26)(17,27)(19,25,34,33)(23,29,32,35)(24,31)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,f^c=fg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10682254, #10682255, #10682256, … |
| maximal normal subgroup of | #10682254, #10682255, #10682256, … |
| maximal quotient of | #10688048, #10688052, #10688056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4588);