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 ⋊ #3022 |
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 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)(4,8,10,9)(5,13,15,14)(6,18,19,22)(7,20,21,23)(11,16,25,28)(12,26,27,29)(17,32,34,33)(24,30,35,31);(4,7)(5,12)(6,17)(8,20)(9,23)(10,21)(11,24)(13,26)(14,29)(15,27)(16,30)(18,32)(19,34)(22,33)(25,35)(28,31);(2,3)(4,6)(5,11)(7,17)(8,18)(9,22)(10,19)(12,24)(13,16)(14,28)(15,25)(20,32)(21,34)(23,33)(26,30)(27,35)(29,31);(4,5,10,15)(6,16,19,28)(7,12,21,27)(8,14,9,13)(11,22,25,18)(17,31,34,30)(20,29,23,26)(24,32,35,33)Polycyclic presentation:
2^7,3|a^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,h^b=h^2,e^c=eg51 conjugacy classes — view the full character table.
| maximal subgroup of | #10714201, #10714202, #10714208, … |
| maximal normal subgroup of | #10714201, #10714202, #10714208, … |
| maximal quotient of | #10767588, #10767619, #10767666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15992);