Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#343 ⋊ C2 |
| Sylow | C3 ⋊ #1860 |
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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)(8,11,14,10)(9,16,19,15)(12,23,13,21)(17,22,18,20);(2,3)(4,6,7,5)(8,10,14,11)(9,15,19,16)(12,23,13,21)(17,22,18,20);(2,3)(4,5,7,6)(8,9,14,19)(10,20,11,22)(12,18,13,17)(15,23,16,21)Polycyclic presentation:
2^7,3|a^2=f,b^2=f,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,d^b=dg,h^b=h^2,e^c=eg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1860, C2×#69003, #10796053, … |
| maximal normal subgroup of | D3×#1860, C2×#69003, #10796053, … |
| maximal quotient of | #10689080, #10689094, #10689245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1579);