D₉×SL(2,𝔽₅) #72228344

order	2160
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

direct product

D₉×SL(2,𝔽₅)

Splittings

derived

C₉×SL(2,𝔽₅) ⋊ C₂

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉×A₅
commutator, hypocenter	C₉×SL(2,𝔽₅)	C₂
Frattini, socle	C₂×C₃	D₃×A₅
Fitting, cosocle	C₂×C₉	C₂×A₅
LCS	G ▷ C₉×SL(2,𝔽₅)
UCS	C₁ ◁ C₂

101 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 216

A minimal faithful permutation representation — 2 generators on 33 points:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

SL(2,𝔽₅)×SL(2,𝔽₈)

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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

D9×SL(2,𝔽5) #72228344