Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#108 ⋊ C2 |
| Sylow | C3 ⋊ #3067 |
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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)(4,8,10,9)(5,13,15,14)(6,18,20,19)(7,22,23,24)(11,26,27,16)(12,28,29,21)(17,32,33,34)(25,35,31,30);(2,3)(4,7)(5,12)(6,17)(8,22)(9,24)(10,23)(11,25)(13,28)(14,21)(15,29)(16,30)(18,32)(19,34)(20,33)(26,35)(27,31);(4,6,8,18,10,20,9,19)(5,11,14,16,15,27,13,26)(7,17,22,32,23,33,24,34)(12,25,21,30,29,31,28,35);(2,3)(4,5)(6,16)(7,21)(8,13)(9,14)(10,15)(11,18)(12,22)(17,31)(19,27)(20,26)(23,28)(24,29)(25,33)(30,32)(34,35)Polycyclic presentation:
2^7,3|b^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,f^c=fg,h^c=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10712144, #10712146, #10712200, … |
| maximal normal subgroup of | #10712144, #10712146, #10712200, … |
| maximal quotient of | #10777430, #10777458, #10777499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11832);