Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1353 |
116 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2)(4,5)(6,10)(7,9)(8,11)(12,14)(13,17,20,27)(15,23)(16,24)(18,26,19,21)(22,25);(2,3)(5,8,9,10)(12,13,15,19,16,20,25,18)(14,21,23,17,24,26,22,27)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,d^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,c^b=cf,d^b=defg,h^b=h^2,d^c=dg45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1353, C2×#67459, #10705492, … |
| maximal normal subgroup of | D3×#1353, C2×#67459, #10705492, … |
| maximal quotient of | #10681982, #10682006, #10682311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 35);