Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1322 |
108 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 43 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) = 192 |
A minimal faithful permutation representation — 2 generators on 27 points:
(2,3)(4,6,7,11)(5,8,9,10);(1,2,3)(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,b^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,d^b=de,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1322, C2×#67524, #10704319, … |
| maximal normal subgroup of | D3×#1322, C2×#67524, #10704319, … |
| maximal quotient of | #10681821, #10681823, #10681825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 100);