Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#536 ⋊ C2 |
| Sylow | C3 ⋊ #3028 |
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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)(4,8,9,20)(5,12,13,19)(6,15,16,30)(7,17,18,32)(10,22,23,29)(11,24,25,31)(14,27,28,35)(21,33,26,34);(4,7)(5,11)(6,14)(8,17)(9,18)(10,21)(12,24)(13,25)(15,27)(16,28)(19,31)(20,32)(22,33)(23,26)(29,34)(30,35);(2,3)(4,6)(5,10)(7,14)(8,15)(9,16)(11,21)(12,22)(13,23)(17,27)(18,28)(19,29)(20,30)(24,33)(25,26)(31,34)(32,35);(4,5,9,13)(6,10,16,23)(7,11,18,25)(8,19,20,12)(14,26,28,21)(15,29,30,22)(17,31,32,24)(27,33,35,34)Polycyclic presentation:
2^7,3|a^2=g,d^2=g,b^a=be,c^a=cf,d^a=dg,f^b=fg,h^b=h^2,e^c=eg51 conjugacy classes — view the full character table.
| maximal subgroup of | #10714175, #10714176, #10714182, … |
| maximal normal subgroup of | #10714175, #10714176, #10714182, … |
| maximal quotient of | #10769223, #10769225, #10769230, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15993);