C₃₇×#1753 #17990571

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₃₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₃₇×#1753

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂³
commutator	C₂²	C₂×C₄²×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle	C₂³×C₃₇	C₂²×C₄
prime radical	C₂⁴×C₃₇	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇ ◁ G

348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 3 generators on 53 points:

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

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#13128, C₂×C₃₇×#1753, C₃₇×#20383, …
maximal normal subgroup of	C₃₇×#13128, C₂×C₃₇×#1753, C₃₇×#20383, …
maximal quotient of	C₃₇×#8146, C₃₇×#8147, C₃₇×#8148, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 485);

C37×#1753 #17990571