C₅₉×D₃₉ #17987178

order	4602
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₉×D₃₉
unambiguous semidirect product	C₃⋊(D₁₃×C₅₉)
unambiguous semidirect product	C₁₃⋊(D₃×C₅₉)

Splittings

Fitting, socle, Hall	C₃×C₁₃×C₅₉ ⋊ C₂
derived, Hall	C₃×C₁₃ ⋊ C₂×C₅₉
Hall	C₁₃×C₅₉ ⋊ D₃
Hall	C₃×C₅₉ ⋊ D₁₃
Sylow	C₁₃ ⋊ D₃×C₅₉
Sylow	C₃ ⋊ D₁₃×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅₉	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₅₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₅₉	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₅₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 2301

A minimal faithful permutation representation — 2 generators on 75 points:

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

Conjugacy classes & character table

1239 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅₉×D₁₁₇, C₅₉×C₃⋊(D₁₃⋊C₃), C₅₉×C₃⋊D₃₉, …
maximal normal subgroup of	C₅₉×C₃⋊(D₁₃⋊C₃), C₃×C₅₉×D₃₉, C₅×C₅₉×D₃₉, …
maximal quotient of	C₅₉×D₁₁₇, C₅₉×C₃⋊D₃₉, C₃×C₅₉×D₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4602, 8);

C59×D39 #17987178