Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4487 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1384 |
132 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 132 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:
(2,3)(4,6,8,19,24,33,22,31,10,18,21,32,9,20,7,17)(5,11,13,27,25,34,12,16,15,26,29,35,14,28,23,30);(1,2,3)(4,5)(6,16,18,30)(7,13)(8,23)(9,25)(10,15)(11,17,26,31)(12,21)(14,24)(19,34,32,28)(20,35,33,27)(22,29)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=f,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,d^b=dg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1384, C2×#67725, #10710471, … |
| maximal normal subgroup of | D3×#1384, C2×#67725, #10710471, … |
| maximal quotient of | #10682062, #10682110, #10682112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 301);