C₃₇×#3550 #17992368

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

Aliases

direct product

C₃₇×#3550

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₇
prime radical	C₃₇×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

1002 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)(46,47,51,49)(48,54,56,52)(50,57,58,53)(55,59,61,60);(39,42)(43,45)(46,48,51,56)(47,52,49,54)(50,55,58,61)(53,59,57,60);(38,39,41,42)(40,43,44,45);(38,40)(39,43)(41,44)(42,45)(46,49,51,47)(48,52,56,54)(50,57,58,53)(55,59,61,60);(46,50,51,58)(47,53,49,57)(48,55,56,61)(52,59,54,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#8492, C₃₇×#8496, C₃₇×#8531, …
maximal normal subgroup of	C₃₇×#8492, C₃₇×#8496, C₃₇×#8531, …
maximal quotient of	C₃₇×#34368, C₃₇×#34374, C₃₇×#34413, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2282);

C37×#3550 #17992368