Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×#104 ⋊ C2 |
| Sylow | C3 ⋊ #2040 |
290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 290 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)(4,6,7,5)(9,15)(10,19)(12,13)(16,17)(20,21)(22,23);(4,5)(6,7)(8,10)(9,14)(11,20)(12,21)(13,19)(15,23)(16,18)(17,22);(2,3)(5,6)(8,9)(10,18)(11,16)(12,15)(13,17)(14,20)(19,23)(21,22)Polycyclic presentation:
2^7,3|c^2=dg,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,c^b=cf,f^b=fg,e^c=eg,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2040, C2×#70362, #10822832, … |
| maximal normal subgroup of | D3×#2040, C2×#70362, #10822832, … |
| maximal quotient of | #10698515, #10698520, #10698522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2938);