C₂×C₅²×C₇×C₄₇ #30657882

order	16450
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₅

Aliases

abelian

C₂×C₅²×C₇×C₄₇

Subgroups

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

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 16450

A minimal faithful permutation representation — 2 generators on 66 points:

(1,2)(3,4,5,6,7)(13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(8,9,10,11,12)

Conjugacy classes & character table

16450 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₇⋊(C₄₇⋊#1039), C₄₇×C₇⋊#1039, C₇×C₄₇⋊#1039, …
socle of	C₄×C₅²×C₇×C₄₇, C₇⋊(C₄₇⋊#1039), C₄₇×C₇⋊#1039, …
maximal subgroup of	C₄×C₅²×C₇×C₄₇, C₇⋊(C₄₇⋊#1039), C₄₇×C₇⋊#1039, …
maximal normal subgroup of	C₄×C₅²×C₇×C₄₇, C₇⋊(C₄₇⋊#1039), C₄₇×C₇⋊#1039, …
maximal quotient of	C₄×C₅²×C₇×C₄₇, C₂²×C₅²×C₇×C₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16450, 9);

C2×C52×C7×C47 #30657882