Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#430 ⋊ C2 |
| Sylow | C3 ⋊ #2916 |
440 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 209 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 — 4 generators on 35 points:
(1,2,3)(7,20)(12,26)(16,30)(21,22)(24,34)(27,33)(28,35)(31,32);(2,3)(4,7)(5,12)(6,16)(8,21)(9,22)(10,20)(11,24)(13,27)(14,26)(15,28)(17,31)(18,32)(19,30)(23,33)(25,34)(29,35);(2,3)(4,6,8,17,10,19,9,18)(5,11,13,15,14,25,23,29)(7,16,21,31,20,30,22,32)(12,24,27,28,26,34,33,35);(4,5,9,13,10,14,8,23)(6,15,18,25,19,29,17,11)(7,12,22,27,20,26,21,33)(16,28,32,34,30,35,31,24)Polycyclic presentation:
2^7,3|a^2=f,b^2=e,e^2=g,f^2=g,b^a=be,e^a=eg,h^b=h^2,d^c=dg,h^c=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | #10813705, #10813708, #10813713, … |
| maximal normal subgroup of | #10813705, #10813708, #10813713, … |
| maximal quotient of | #10764175, #10764180, #10764228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11836);