D₅×C₁₇×D₅₉ #34095411

order	20060
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₅×C₁₇×D₅₉
unambiguous semidirect product	(D₅×C₅₉)⋊(C₂×C₁₇)
unambiguous semidirect product	(C₅×D₅₉)⋊(C₂×C₁₇)
unambiguous semidirect product	D₂₉₅⋊(C₂×C₁₇)

Splittings

Fitting, socle, Hall	C₅×C₁₇×C₅₉ ⋊ C₂²
derived, Hall	C₅×C₅₉ ⋊ C₂²×C₁₇
Hall	C₁₇×C₅₉ ⋊ C₂×D₅
Hall	C₅×C₁₇ ⋊ C₂×D₅₉
Sylow	C₅₉ ⋊ C₂×D₅×C₁₇
Sylow	C₅ ⋊ C₂×C₁₇×D₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	D₅×D₅₉
commutator, cosocle, hypocenter	C₅×C₅₉	C₂²×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₅₉	C₂²
LCS	G ▷ C₅×C₅₉
UCS	C₁ ◁ C₁₇

40 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:

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

Conjugacy classes & character table

2108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20060, 21);

D5×C17×D59 #34095411