C₃₇×#1397 #17990215

order	4736
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#1397

Subgroups

	subgroup	G/H
center	C₂×C₁₆×C₃₇	C₂²
commutator	C₂	C₄×C₁₆×C₃₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₃₇
socle, prime radical	C₂²×C₃₇	C₂×C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₃₇ ◁ G

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 2 generators on 73 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)(42,43,44,49,45,50,52,61,46,51,53,62,55,63,64,71,47,48,54,58,56,59,65,68,57,60,66,69,67,70,72,73);(38,39,40,41)(43,48)(49,58)(50,59)(51,60)(61,68)(62,69)(63,70)(71,73)

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7330, C₃₇×#7332, C₃₇×#7380, …
maximal normal subgroup of	C₃₇×#7330, C₃₇×#7332, C₃₇×#7380, …
maximal quotient of	C₃₇×#7329, C₃₇×#7331, C₃₇×#7465, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 129);

C37×#1397 #17990215