Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #69507 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2026 |
258 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 31 points:
(2,3)(5,7)(16,18,19,25)(17,22,21,30)(20,29,27,26)(23,31,28,24);(1,2,3)(4,5)(6,7)(8,10,11,15)(9,12,13,14)(17,21)(22,30)(23,28)(24,31);(8,9,11,13)(10,14,15,12)(16,17,19,21)(18,24,25,31)(20,28,27,23)(22,29,30,26)Polycyclic presentation:
2^7,3|a^2=d,b^2=dg,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,e^c=eg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2026, C2×#71744, #10822478, … |
| maximal normal subgroup of | D3×#2026, C2×#71744, #10822478, … |
| maximal quotient of | #10698179, #10698189, #10698216, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4320);