C₂×C₃×C₇²×C₅₃ #29510035

order	15582
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₇

Aliases

abelian

C₂×C₃×C₇²×C₅₃

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) = 72
transitive degree	μ_t(G) = 15582

A minimal faithful permutation representation — 2 generators on 72 points:

(1,2)(3,4,5)(6,7,8,9,10,11,12)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72);(13,14,15,16,17,18,19)

Conjugacy classes & character table

15582 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃⋊(C₇⋊Dic₃₇₁), C₅₃×C₃⋊(C₇⋊Dic₇), C₇×Dic₁₁₁₃, …
socle of	C₃×C₄×C₇²×C₅₃, C₃⋊(C₇⋊Dic₃₇₁), C₅₃×C₃⋊(C₇⋊Dic₇), …
maximal subgroup of	C₃×C₄×C₇²×C₅₃, C₃⋊(C₇⋊Dic₃₇₁), C₅₃×C₃⋊(C₇⋊Dic₇), …
maximal normal subgroup of	C₃×C₄×C₇²×C₅₃, C₃⋊(C₇⋊Dic₃₇₁), C₅₃×C₃⋊(C₇⋊Dic₇), …
maximal quotient of	C₃×C₄×C₇²×C₅₃, C₂²×C₃×C₇²×C₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15582, 13);

C2×C3×C72×C53 #29510035