Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3240 |
328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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) = 192 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3)(5,11)(9,12)(10,19)(17,18)(20,23,24,25)(21,28,26,29)(22,31,32,33)(27,30,34,35);(2,3)(4,7,8,16)(5,10,11,19)(6,13,14,15)(9,17,12,18)(20,22,24,32)(21,27,26,34)(23,31,25,33)(28,30,29,35);(4,6,8,14)(5,9,11,12)(7,15,16,13)(10,18,19,17)(21,26)(27,34)(28,29)(30,35);(4,5)(6,12)(7,10)(8,11)(9,14)(13,18)(15,17)(16,19)(20,21)(22,30)(23,29)(24,26)(25,28)(27,31)(32,35)(33,34)Polycyclic presentation:
2^7,3|b^2=eg,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | #10692402, #10692404, #10776564, … |
| maximal normal subgroup of | #10692402, #10692404, #10776564, … |
| maximal quotient of | #10804725, #10804935, #10805763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15701);