Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×#102 ⋊ C2 |
| Sylow | C3 ⋊ #2051 |
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(5,7)(8,10,11,20,13,19,12,21)(9,15,16,22,17,23,14,18);(9,14)(10,19)(11,12)(15,18)(16,17)(22,23);(2,3)(4,5)(6,7)(8,9)(10,18)(11,14)(12,16)(13,17)(15,21)(19,22)(20,23)Polycyclic presentation:
2^7,3|c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,e^b=eg,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2051, C2×#70196, #10823066, … |
| maximal normal subgroup of | D3×#2051, C2×#70196, #10823066, … |
| maximal quotient of | #10698866, #10698873, #10698894, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2772);