Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ #3414 |
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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)(4,7,10,9)(5,13,12,24)(6,16,18,25)(8,19,23,22)(11,27,26,28)(14,20,29,34)(15,32,31,30)(17,21,33,35);(5,12)(11,26)(13,24)(14,29)(15,31)(20,34)(27,28)(30,32);(2,3)(4,6)(5,11)(7,16)(8,21)(9,25)(10,18)(12,26)(13,27)(14,30)(15,20)(17,22)(19,33)(23,35)(24,28)(29,32)(31,34);(2,3)(4,5)(6,15)(7,13)(8,20)(9,24)(10,12)(11,17)(14,22)(16,32)(18,31)(19,29)(21,27)(23,34)(25,30)(26,33)(28,35)Polycyclic presentation:
2^7,3|d^2=g,e^2=fg,f^2=g,b^a=be,c^a=cg,e^a=ef,f^a=fg,h^a=h^2,e^b=ef,f^b=fg,h^b=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10712306, #10712308, #10712327, … |
| maximal normal subgroup of | #10712306, #10712308, #10712327, … |
| maximal quotient of | #10948093, #10948226, #10948499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14585);