C₃₇×#1442 #17990260

order	4736
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#1442

Subgroups

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

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 4736

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)(42,43,45,44)(47,48)(50,51,52,53);(39,41)(43,44)(46,47,49,48);(38,39)(40,41)(42,44,45,43)(46,48,49,47)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7122, C₃₇×#8867, C₃₇×#8869, …
maximal normal subgroup of	C₃₇×#7122, C₃₇×#8867, C₃₇×#8869, …
maximal quotient of	C₃₇×#7556, C₃₇×#7557, C₃₇×#11255, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 174);

C37×#1442 #17990260