Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×#349 ⋊ C2 |
| Sylow | C3 ⋊ #1321 |
112 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 33 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)(5,11)(7,20)(8,22)(9,16)(10,18)(12,28)(13,26)(14,27)(15,19)(17,24)(21,25)(23,33)(29,34)(30,32)(31,35);(1,2,3)(4,5,8,13,9,12,23,29,10,14,24,31,7,19,21,30)(6,15,17,32,16,11,25,26,18,28,22,34,20,27,33,35)Polycyclic presentation:
2^7,3|a^2=d,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=cg,d^b=deg,h^b=h^2,d^c=dg48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1321, C2×#67531, #10704313, … |
| maximal normal subgroup of | D3×#1321, C2×#67531, #10704313, … |
| maximal quotient of | #10681809, #10681811, #10681813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 107);