Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #2975 |
452 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(5,9)(8,10);(6,11)(8,10)(13,16)(17,19);(4,6)(5,8)(7,11)(9,10)(13,16)(17,19);(2,3)(4,5)(6,10)(7,9)(8,11)(12,13,15,17,14,16,18,19)Polycyclic presentation:
2^7,3|a^2=f,f^2=g,b^a=be,c^a=cg,d^a=deg,h^a=h^2,c^b=ceg84 conjugacy classes — view the full character table.
| maximal subgroup of | #10689058, #10689061, #10689201, … |
| maximal normal subgroup of | #10689058, #10689061, #10689201, … |
| maximal quotient of | #10793865, #10793935, #10794222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14880);