Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1314 |
140 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(4,6)(5,8)(7,11)(9,10);(2,3)(4,5)(6,10,11,8)(7,9)(12,13,14,17,15,18,20,23,16,19,21,24,22,25,26,27)Polycyclic presentation:
2^7,3|a^2=d,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^2,d^b=de84 conjugacy classes — view the full character table.
| maximal subgroup of | #10681805, #10681806, #10681807, … |
| maximal normal subgroup of | #10681805, #10681806, #10681807, … |
| maximal quotient of | #10681806, #10681808, #10681810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 249);