Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#101 ⋊ C2 |
| Sylow | C3 ⋊ #1901 |
338 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 85 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:
(2,3)(5,7);(1,2,3)(8,10,16,18,12,17,11,19)(9,13,15,23,14,21,22,20);(4,5)(6,7)(8,9,11,15,12,14,16,22)(10,13,18,20,17,21,19,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=dfg,f^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,f^b=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1901, C2×#70115, #10797015, … |
| maximal normal subgroup of | D3×#1901, C2×#70115, #10797015, … |
| maximal quotient of | #10690565, #10690570, #10690585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2691);