Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1382 |
132 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 2 generators on 39 points:
(1,2)(8,10,12,21,25,36,26,37,14,23,11,20,13,22,28,38)(9,15,16,19,29,33,27,39,18,31,32,35,17,30,24,34);(2,3)(4,5,6,7)(8,9)(10,19)(11,24)(12,27)(13,29)(14,18)(15,20)(16,26)(17,25)(21,31)(22,39)(23,35)(28,32)(30,38)(33,37)(34,36)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=fg,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^a=h^2,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1382, C2×#67729, #10710082, … |
| maximal normal subgroup of | D3×#1382, C2×#67729, #10710082, … |
| maximal quotient of | #10682058, #10682101, #10682106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 305);