C₃₇×#3559 #17992377

order	4736
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃₇ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₃₇×#3559

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 5 generators on 61 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)(39,42)(40,44)(46,47)(48,55)(49,52)(50,58)(51,54)(53,59)(56,60)(57,61);(39,42)(43,45)(46,48,51,49)(47,52,54,55)(50,56,59,57)(53,60,58,61);(38,39)(40,43)(41,42)(44,45)(46,49,51,48)(47,52,54,55)(50,57,59,56)(53,60,58,61);(38,40,41,44)(39,43,42,45)(46,47)(48,55)(49,52)(50,53)(51,54)(56,61)(57,60)(58,59);(46,50)(47,53)(48,56)(49,57)(51,59)(52,60)(54,58)(55,61)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8486, C₃₇×#8513, C₃₇×#18244, …
maximal normal subgroup of	C₃₇×#8486, C₃₇×#8513, C₃₇×#18244, …
maximal quotient of	C₃₇×#34378, C₃₇×#34382, C₃₇×#34398, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2291);

C37×#3559 #17992377