C₂×D₅×C₁₇×C₅₉ #34095422

order	20060
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₇×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₅×C₁₇×C₅₉
unambiguous semidirect product	C₅⋊(C₂²×C₁₇×C₅₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₁₇×C₅₉)

Splittings

Fitting, socle	C₂×C₅×C₁₇×C₅₉ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂²×C₁₇×C₅₉
Hall	C₅×C₁₇×C₅₉ ⋊ C₂²
Hall	C₅×C₅₉ ⋊ C₂²×C₁₇
Hall	C₅×C₁₇ ⋊ C₂²×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₇×C₅₉	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₁₇×C₅₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₇×C₅₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₁₇×C₅₉

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 10030

A minimal faithful permutation representation — 2 generators on 83 points:

(2,3)(4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81);(1,2,4,5,3)(82,83)

Conjugacy classes & character table

8024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20060, 32);

C2×D5×C17×C59 #34095422