C₃₇×#1439 #17990257

order	4736
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₇×#1439

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₃₇	C₂³
commutator	C₂³	C₂²×C₄×C₃₇
Frattini, cosocle	C₂⁴	C₂³×C₃₇
prime radical	C₂⁵×C₃₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₇ ◁ G

780 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)(43,45)(46,47,48,49)(51,53);(39,41)(43,45)(50,51,52,53);(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7250, C₃₇×#8403, C₃₇×#8405, …
maximal normal subgroup of	C₃₇×#7250, C₃₇×#8403, C₃₇×#8405, …
maximal quotient of	C₃₇×#7555, C₃₇×#7556, C₃₇×#7557, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 171);

C37×#1439 #17990257