Finite Group Databasebeta

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C₂×#20280433 #27551003

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

5194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 79 points:

(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)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(67,75)(70,77)(73,79)(76,78);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(57,59)(61,63)(64,67)(65,70)(66,73)(68,75)(69,76)(71,77)(72,78)(74,79);(60,61)(62,63)(64,66,68,74)(65,69,71,72)(67,73,75,79)(70,76,77,78);(56,57)(58,59)(64,65,68,71)(66,72,74,69)(67,70,75,77)(73,78,79,76);(54,55)

Conjugacy classes & character table

1208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 336479);