Finite Group Databasebeta

?

← Prev (#64442) Next (#64444) →

C₂²⋊D₃₇ #64443

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(39,41);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)

Polycyclic presentation:

2^3,37|b^a=bc,d^a=d^36

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(296, 8);