C₃₇×#1745 #17990563

order	4736
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₃₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₃₇×#1745

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₃₇	C₂³
commutator	C₂²	C₂×C₄²×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle, prime radical	C₂³×C₃₇	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₇ ◁ G

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 generators on 57 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)(44,47)(45,46)(48,49)(50,51,52,55,53,54,56,57);(38,39,40,41)(43,46)(47,49);(42,44,45,48)(43,47,46,49)(51,54)(55,57)

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7023, C₃₇×#7043, C₃₇×#7048, …
maximal normal subgroup of	C₃₇×#7023, C₃₇×#7043, C₃₇×#7048, …
maximal quotient of	C₃₇×#8132, C₃₇×#8134, C₃₇×#8136, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 477);

C37×#1745 #17990563