C₂×C₃×C₄×C₅₃ #11929681

order	1272
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 832
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂×C₃×C₄×C₅₃
multiplicative	(ℤ/1391)ˣ, (ℤ/2782)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₃×C₅₃
socle, prime radical	C₂²×C₃×C₅₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 1272

A minimal faithful permutation representation — 2 generators on 62 points:

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

Conjugacy classes & character table

1272 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄²×C₅₃, C₂×C₃×C₈×C₅₃, C₂²×C₃×C₄×C₅₃, …
maximal normal subgroup of	C₃×C₄²×C₅₃, C₂×C₃×C₈×C₅₃, C₂²×C₃×C₄×C₅₃, …
maximal quotient of	C₃×C₄²×C₅₃, C₂×C₃×C₈×C₅₃, C₂²×C₃×C₄×C₅₃, …
automorphism group of	C₁₃×C₁₀₇, C₂×C₁₃×C₁₀₇
outer automorphism group of	C₁₃×C₁₀₇, C₂×C₁₃×C₁₀₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1272, 30);

C2×C3×C4×C53 #11929681