Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1831 |
260 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 129 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) = 384 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(4,6,7,5)(17,21)(20,23);(2,3)(4,5,7,6)(16,18,19,22)(17,20,21,23);(5,6)(8,9,10,12,11,13,14,15)(16,17)(18,20)(19,21)(22,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=e,c^2=d,f^2=g,b^a=bd,c^a=ce,h^b=h^2,h^c=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | #10681821, #10687878, #10687879, … |
| maximal normal subgroup of | #10681821, #10687878, #10687879, … |
| maximal quotient of | #10688832, #10688836, #10688847, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3019);