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C₂×C₃×C₅×C₇²×C₁₃ #34062056

order	19110
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

C₂×C₃×C₅×C₇²×C₁₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 19110

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2)(3,4,5)(6,7,8,9,10)(11,12,13,14,15,16,17)(25,26,27,28,29,30,31,32,33,34,35,36,37);(18,19,20,21,22,23,24)

Conjugacy classes & character table

19110 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃⋊(C₇⋊Dic₄₅₅), C₁₃×C₃⋊(C₇⋊Dic₃₅), C₇×Dic₁₃₆₅, …
socle of	C₃×C₄×C₅×C₇²×C₁₃, C₃⋊(C₇⋊Dic₄₅₅), C₁₃×C₃⋊(C₇⋊Dic₃₅), …
maximal subgroup of	C₃×C₄×C₅×C₇²×C₁₃, C₃⋊(C₇⋊Dic₄₅₅), C₁₃×C₃⋊(C₇⋊Dic₃₅), …
maximal normal subgroup of	C₃×C₄×C₅×C₇²×C₁₃, C₃⋊(C₇⋊Dic₄₅₅), C₁₃×C₃⋊(C₇⋊Dic₃₅), …
maximal quotient of	C₃×C₄×C₅×C₇²×C₁₃, C₂²×C₃×C₅×C₇²×C₁₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 49);