#157×C₅₉ #14523783

order	2124
isoclinism	isoclinic class of #157
automorphism	?
homology	Abelianization (H₁) = C₄×C₅₉ · Schur multiplier (H₂) = C₃

Aliases

direct product

#157×C₅₉

Splittings

Fitting, socle, Hall	C₃²×C₅₉ ⋊ C₄
derived, Sylow	C₃² ⋊ C₄×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅₉	#157
commutator, hypocenter	C₃²	C₄×C₅₉
Frattini	C₁	G
Fitting, socle	C₃²×C₅₉	C₄
prime radical	C₃⋊D₃×C₅₉	C₂
cosocle	C₃⋊D₃	C₂×C₅₉
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅₉

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 354

A minimal faithful permutation representation — 2 generators on 65 points:

(1,2)(3,5,6,4)(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);(1,3,6)(2,5,4)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×#157×C₅₉, C₅₉×C₇⋊#157, C₁₁×#157×C₅₉, …
maximal normal subgroup of	C₇×#157×C₅₉, C₁₁×#157×C₅₉, C₁₃×#157×C₅₉, …
maximal quotient of	C₇×#157×C₅₉, C₅₉×C₇⋊#157, C₁₁×#157×C₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2124, 23);

#157×C59 #14523783