Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#410 ⋊ C2 |
| Sylow | C3 ⋊ #2884 |
716 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 209 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)(4,8,9,21)(5,12,13,27)(6,16,17,33)(7,18,19,20)(10,23,14,29)(11,24,25,26)(15,30,31,32)(22,34,28,35);(2,3)(4,7,9,19)(5,11,13,25)(6,15,17,31)(8,20,21,18)(10,22,14,28)(12,26,27,24)(16,32,33,30)(23,35,29,34);(4,6)(5,10)(7,15)(8,16)(9,17)(11,22)(12,23)(13,14)(18,30)(19,31)(20,32)(21,33)(24,34)(25,28)(26,35)(27,29);(4,5)(6,14,17,10)(7,11)(8,12)(9,13)(15,28,31,22)(16,29,33,23)(18,24)(19,25)(20,26)(21,27)(30,35,32,34)Polycyclic presentation:
2^7,3|a^2=f,c^2=g,d^2=g,b^a=be,e^a=eg,f^b=fg,d^c=dg,h^c=h^263 conjugacy classes — view the full character table.
| maximal subgroup of | #10712778, #10712780, #10712782, … |
| maximal normal subgroup of | #10712778, #10712780, #10712782, … |
| maximal quotient of | #10761013, #10761015, #10761017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11265);