Finite Group Databasebeta

← Prev (#30633491) Next (#30633493) →

C₂×C₃×C₅×C₇²×C₁₁ #30633492

order	16170
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

C₂×C₃×C₅×C₇²×C₁₁

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) = 35
transitive degree	μ_t(G) = 16170

A minimal faithful permutation representation — 2 generators on 35 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);(18,19,20,21,22,23,24)

Conjugacy classes & character table

16170 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃⋊(C₇⋊Dic₃₈₅), C₁₁×C₃⋊(C₇⋊Dic₃₅), C₇×Dic₁₁₅₅, …
socle of	C₃×C₄×C₅×C₇²×C₁₁, C₃⋊(C₇⋊Dic₃₈₅), C₁₁×C₃⋊(C₇⋊Dic₃₅), …
maximal subgroup of	C₃×C₄×C₅×C₇²×C₁₁, C₃⋊(C₇⋊Dic₃₈₅), C₁₁×C₃⋊(C₇⋊Dic₃₅), …
maximal normal subgroup of	C₃×C₄×C₅×C₇²×C₁₁, C₃⋊(C₇⋊Dic₃₈₅), C₁₁×C₃⋊(C₇⋊Dic₃₅), …
maximal quotient of	C₃×C₄×C₅×C₇²×C₁₁, C₂²×C₃×C₅×C₇²×C₁₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 37);