C₃₇×#1920 #17990738

order	4736
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃₇×#1920

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

230 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)(38,39,41,40)(42,43)(44,47)(45,46)(48,49)(50,51,53,56)(52,54,57,55);(38,40,41,39)(43,46)(47,49);(42,44,45,48)(43,47,46,49)(51,54)(52,57)(55,56)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#1920, C₃₇×#21032, C₃₇×#21033, …
maximal normal subgroup of	C₂×C₃₇×#1920, C₃₇×#21032, C₃₇×#21033, …
maximal quotient of	C₃₇×#9535, C₃₇×#9539, C₃₇×#10806, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 652);

C37×#1920 #17990738