Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1388 |
124 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2)(4,6,9,20,10,21,26,18,11,22,25,34,8,19,7,24)(5,12,15,29,14,28,13,31,16,30,23,35,27,33,32,17);(2,3)(4,5,8,14,11,16,10,27)(6,17,19,29,22,31,21,35)(7,23,25,32,26,15,9,13)(12,20,28,24,30,34,33,18)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^2,c^b=cg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1388, C2×#67734, #10710454, … |
| maximal normal subgroup of | D3×#1388, C2×#67734, #10710454, … |
| maximal quotient of | #10682066, #10682118, #10682119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 310);