C₂²×C₁₉⋊C₃×C₅₉ #27212116

order	13452
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂²×C₁₉⋊C₃×C₅₉

Splittings

Fitting, socle, Hall	C₂²×C₁₉×C₅₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₂²×C₃×C₅₉
Hall	C₁₉×C₅₉ ⋊ C₂²×C₃
Hall	C₂²×C₁₉ ⋊ C₃×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₅₉	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂²×C₃×C₅₉
Frattini	C₁	G
Fitting, socle	C₂²×C₁₉×C₅₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₅₉

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 82
transitive degree	μ_t(G) = 4484

A minimal faithful permutation representation — 2 generators on 82 points:

(2,3,5)(4,7,8)(6,10,9)(11,15,13)(12,16,14)(17,19,18)(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)(81,82);(1,2,4,8,13,18,15,3,6,11,16,5,9,14,7,12,17,19,10)(79,80)

Conjugacy classes & character table

2124 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13452, 27);

C22×C19⋊C3×C59 #27212116