C₂×C₅×C₇²×C₃₇ #31827408

order	18130
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

abelian

C₂×C₅×C₇²×C₃₇

Subgroups

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

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 18130

A minimal faithful permutation representation — 2 generators on 58 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14)(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);(15,16,17,18,19,20,21)

Conjugacy classes & character table

18130 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₇⋊Dic₁₂₉₅, C₃₇×C₇⋊Dic₃₅, C₇×Dic₁₂₉₅, …
socle of	C₄×C₅×C₇²×C₃₇, C₇⋊Dic₁₂₉₅, C₃₇×C₇⋊Dic₃₅, …
maximal subgroup of	C₄×C₅×C₇²×C₃₇, C₇⋊Dic₁₂₉₅, C₃₇×C₇⋊Dic₃₅, …
maximal normal subgroup of	C₄×C₅×C₇²×C₃₇, C₇⋊Dic₁₂₉₅, C₃₇×C₇⋊Dic₃₅, …
maximal quotient of	C₄×C₅×C₇²×C₃₇, C₂²×C₅×C₇²×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18130, 9);

C2×C5×C72×C37 #31827408