C₃₇×#1830 #17990648

order	4736
nilpotency class	3
isoclinism	isoclinic class of #1828
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#1830

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	#381
commutator	C₂³	C₂²×C₄×C₃₇
Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
prime radical	C₂³×C₃₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 1184

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

Conjugacy classes & character table

1073 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#12729, C₃₇×#12730, C₂×C₃₇×#1830, …
maximal normal subgroup of	C₃₇×#12729, C₃₇×#12730, C₂×C₃₇×#1830, …
maximal quotient of	C₃₇×#8735, C₃₇×#8737, C₃₇×#8753, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 562);

C37×#1830 #17990648