Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #1830 |
236 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 73 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 — 3 generators on 35 points:
(1,2,3)(4,7)(5,11,12,18)(6,15)(8,20)(9,19)(10,23,14,29)(13,26,27,32)(16,31)(17,30)(21,33)(22,25)(24,34,28,35);(2,3)(4,6,9,17)(5,10,12,14)(7,15,19,30)(8,21,22,16)(11,23,18,29)(13,28,27,24)(20,33,25,31)(26,35,32,34);(4,5,8,13,9,12,22,27)(6,14,16,28,17,10,21,24)(7,18,20,32,19,11,25,26)(15,23,31,34,30,29,33,35)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^2,e^c=eg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1830, C2×#69029, #10795055, … |
| maximal normal subgroup of | D3×#1830, C2×#69029, #10795055, … |
| maximal quotient of | #10688648, #10688654, #10688708, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1605);