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C₂₃×H(7,𝔽₂) #15671213

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

5992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 39 points:

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

Conjugacy classes & character table

1495 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2326);