Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#344 ⋊ C2 |
| Sylow | C3 ⋊ #2009 |
348 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 71 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)(4,7,10,23)(5,12,15,29)(6,17,19,33)(8,22,9,21)(11,25,26,27)(13,20,14,28)(16,31,30,35)(18,34,24,32);(2,3)(4,6)(5,11)(7,17)(8,24)(9,18)(10,19)(12,27)(13,30)(14,16)(15,26)(20,31)(21,34)(22,32)(23,33)(25,29)(28,35);(2,3)(4,5)(6,16)(7,20)(8,14)(9,13)(10,15)(11,18)(12,22)(17,25)(19,30)(21,29)(23,28)(24,26)(27,33)(31,32)(34,35)Polycyclic presentation:
2^7,3|c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,d^b=dg,h^b=h^2,d^c=dg,e^c=eg,h^c=h^245 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2009, C2×#69031, #10822192, … |
| maximal normal subgroup of | D3×#2009, C2×#69031, #10822192, … |
| maximal quotient of | #10695505, #10695519, #10695533, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1607);