Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2115 |
220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 220 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)(6,15)(10,14)(16,18)(17,29)(22,26)(23,28)(30,31)(33,35);(4,6)(5,10)(7,18)(8,17)(9,15)(11,14)(12,26)(13,23)(16,20)(19,31)(21,29)(22,24)(25,28)(27,35)(30,32)(33,34);(2,3)(4,5,7,12,8,13,19,27,9,11,20,24,21,25,32,34)(6,14,16,26,17,28,30,35,15,10,18,22,29,23,31,33)Polycyclic presentation:
2^7,3|a^2=e,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^2,c^b=cg,e^b=eg84 conjugacy classes — view the full character table.
| maximal subgroup of | #10682194, #10682195, #10682197, … |
| maximal normal subgroup of | #10682194, #10682195, #10682197, … |
| maximal quotient of | #10704252, #10704324, #10704393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4583);