C₅₉×#66776 #34095407

order	20060
isoclinism	isoclinic class of #66776
automorphism	?
homology	Abelianization (H₁) = C₄×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₅₉×#66776

Splittings

Fitting, socle, Hall	C₅×C₁₇×C₅₉ ⋊ C₄
derived, Hall	C₅×C₁₇ ⋊ C₄×C₅₉
Hall	C₁₇×C₅₉ ⋊ AGL(1,𝔽₅)
Hall	C₅×C₅₉ ⋊ #595
Sylow	C₁₇ ⋊ AGL(1,𝔽₅)×C₅₉
Sylow	C₅ ⋊ C₅₉×#595

Subgroups

	subgroup	G/H
center, hypercenter	C₅₉	#66776
commutator, hypocenter	C₅×C₁₇	C₄×C₅₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₅₉	C₄
prime radical	C₅₉×D₈₅	C₂
cosocle	D₈₅	C₂×C₅₉
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₅₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 5015

A minimal faithful permutation representation — 2 generators on 81 points:

(2,6,4,3)(5,13,9,8)(7,11,10,12)(14,15,17,16)(19,22,21,20)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81);(1,2,5,10,6,11,15,17,13,8,14,16,12,3,7,9,4)(18,19,22,20,21)

Conjugacy classes & character table

1475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20060, 17);

C59×#66776 #34095407