Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #2231 |
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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)(6,18)(8,22)(9,24)(10,26)(11,27)(13,31)(14,32)(15,33)(16,34)(17,21)(19,29)(20,28)(23,35)(25,30);(4,6,17,23,8,19,10,9)(5,11,25,14,13,28,15,16)(7,18,21,35,22,29,26,24)(12,27,30,32,31,20,33,34);(2,3)(4,5,8,13)(6,16,19,14)(7,20)(9,11,23,28)(10,25,17,15)(12,29)(18,31)(21,32)(22,27)(24,33)(26,34)(30,35)Polycyclic presentation:
2^7,3|a^2=d,b^2=df,e^2=f,f^2=g,b^a=bdfg,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,d^c=dg,e^c=efg,f^c=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | #10709578, #10709580, #10709583, … |
| maximal normal subgroup of | #10709578, #10709580, #10709583, … |
| maximal quotient of | #10711293, #10711884, #10712886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3496);