C₃₇×#3532 #17992350

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

Aliases

direct product

C₃₇×#3532

Subgroups

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

1336 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 592

A minimal faithful permutation representation — 5 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)(40,46)(41,45)(42,44)(43,48)(47,50)(49,52)(51,53);(38,40)(39,43)(41,48)(42,47)(44,51)(45,46)(49,53)(50,52);(39,44)(40,47)(45,52)(48,53);(39,44)(40,48)(43,50)(45,52)(46,51)(47,53);(39,45)(43,46)(44,52)(50,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#12753, C₃₇×#33551, C₂×C₃₇×#3532, …
maximal normal subgroup of	C₃₇×#12753, C₃₇×#33551, C₂×C₃₇×#3532, …
maximal quotient of	C₃₇×#34356, C₃₇×#34406, C₃₇×#34407, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 2264);

C37×#3532 #17992350