C₂²×C₂₉×C₁₃⋊C₃ #17985333

order	4524
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂²×C₂₉×C₁₃⋊C₃

Splittings

Fitting, socle, Hall	C₂²×C₁₃×C₂₉ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₂²×C₃×C₂₉
Hall	C₁₃×C₂₉ ⋊ C₂²×C₃
Hall	C₂²×C₁₃ ⋊ C₃×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₂₉	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₂₉	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₂₉

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 1508

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2)(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)(35,36,38)(37,40,43)(39,42,41)(44,46,45);(3,4)(34,35,37,36,39,43,40,44,46,38,41,45,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	A₄×C₂₉×C₁₃⋊C₃, C₂×D₃×C₂₉×C₁₃⋊C₃, C₂²×C₃×C₂₉×C₁₃⋊C₃, …
maximal normal subgroup of	A₄×C₂₉×C₁₃⋊C₃, C₂²×C₃×C₂₉×C₁₃⋊C₃, C₂²×C₅×C₂₉×C₁₃⋊C₃, …
maximal quotient of	C₂²×C₂₉×C₁₃⋊C₉, C₂×D₃×C₂₉×C₁₃⋊C₃, C₂²×C₃×C₂₉×C₁₃⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4524, 43);

C22×C29×C13⋊C3 #17985333