#72210859

order	2880
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₂

non-solvable

Aliases

No aliases for this group.

Splittings

derived

A₆ ⋊ C₈

Subgroups

	subgroup	G/H
center, Frattini, Fitting, hypercenter	C₄	PGL(2,𝔽₉)
commutator, hypocenter	A₆	C₈
socle, prime radical	C₂×A₆	C₄
cosocle	C₄×A₆	C₂
LCS	G ▷ A₆
UCS	C₁ ◁ C₄

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72224456
maximal normal subgroup of	#72224456
maximal quotient of	GL(2,𝔽₉)

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

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