C₉×C₄₃×#261 #34117447

order	20124
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₉×C₄₃×#261

Splittings

Fitting, Hall	C₉×C₁₃×C₄₃ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₄×C₉×C₄₃
Hall	C₁₃×C₄₃ ⋊ C₄×C₉
Hall	C₉×C₁₃ ⋊ C₄×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₄₃	#261
commutator, hypocenter	C₁₃	C₄×C₉×C₄₃
Frattini	C₃	C₃×C₄₃×#261
Fitting	C₉×C₁₃×C₄₃	C₄
socle	C₃×C₁₃×C₄₃	C₃×C₄
prime radical	C₃×D₁₃×C₄₃	C₂×C₃
cosocle	C₃×D₁₃	C₂×C₃×C₄₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₉×C₄₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 5031

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

(2,6,4,3)(5,13,9,8)(7,10,12,11)(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)(57,58,60,59,61,63,62,64,65);(1,2,5,8,12,6,10,11,3,7,13,9,4)

Conjugacy classes & character table

2709 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20124, 50);

C9×C43×#261 #34117447