C₃₇×#1710 #17990528

order	4736
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₃₇×#1710

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₇	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₃₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ G

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 3 generators on 69 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)(38,39,42,44)(40,46,48,53)(41,49,50,45)(43,51,52,47)(54,55)(56,62)(57,59)(58,66)(60,64)(61,65)(63,68)(67,69);(38,40,41,47,42,48,50,51)(39,43,45,46,44,52,49,53)(55,59)(60,67)(61,66)(62,68);(39,44)(43,52)(45,49)(46,53)(54,56,58,64,57,63,65,69)(55,60,61,62,59,67,66,68)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#7093, C₃₇×#12449, C₃₇×#12450, …
maximal normal subgroup of	C₃₇×#7093, C₃₇×#12449, C₃₇×#12450, …
maximal quotient of	C₃₇×#8816, C₃₇×#9821, C₃₇×#9823, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 442);

C37×#1710 #17990528