Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2098 |
210 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 65 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 — 3 generators on 35 points:
(1,2,3)(4,7)(5,12)(6,16)(8,22)(9,23)(10,25)(11,26)(13,29)(14,20)(15,32)(17,21)(18,34)(19,33)(24,30)(27,35)(28,31);(2,3)(4,6,10,17,9,19,8,18)(5,11,24,15,14,27,13,31)(7,21,25,33,23,34,22,16)(12,28,30,26,20,32,29,35);(4,5,8,13,9,14,10,24)(6,15,17,27,19,31,18,11)(7,20,22,30,23,12,25,29)(16,32,21,35,33,28,34,26)Polycyclic presentation:
2^7,3|a^2=d,b^2=de,d^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^b=h^2,f^c=fg54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682801, #10682803, #10682804, … |
| maximal normal subgroup of | #10682801, #10682803, #10682804, … |
| maximal quotient of | #10700158, #10700165, #10700170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2581);