Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×#101 ⋊ C2 |
| Sylow | C3 ⋊ #3069 |
446 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 446 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)(6,18)(11,26)(16,27)(17,32)(19,20)(25,31)(30,35)(33,34);(2,3)(4,7)(5,12)(6,17)(8,22)(9,24)(10,23)(11,25)(13,21)(14,29)(15,28)(16,30)(18,32)(19,33)(20,34)(26,31)(27,35);(2,3)(4,6,8,19,10,18,9,20)(5,11,13,16,15,26,14,27)(7,17,22,33,23,32,24,34)(12,25,21,30,28,31,29,35);(4,5,10,15)(6,16,18,27)(7,21,23,29)(8,14,9,13)(11,20,26,19)(12,24,28,22)(17,31,32,25)(30,34,35,33)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,h^b=h^2,f^c=fg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | #10832708, #10832718, #10832730, … |
| maximal normal subgroup of | #10832708, #10832718, #10832730, … |
| maximal quotient of | #10777964, #10777975, #10778008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11288);