C₃₇×#2789 #17991607

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₃₇×#2789

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇ ◁ G

352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 4736

A minimal faithful permutation representation — 4 generators on 61 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)(40,44)(41,42)(43,45)(46,47,51,53)(48,50,49,52)(54,55,58,60)(56,57,59,61);(39,42)(43,44)(46,48,51,49)(47,52,53,50)(54,56)(55,57)(58,59)(60,61);(38,40,41,45)(39,43,42,44)(46,49,51,48)(47,52,53,50)(54,57)(55,59)(56,60)(58,61);(38,39)(40,43)(41,42)(44,45)(46,50,51,52)(47,48,53,49)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#12143, C₃₇×#12237, C₃₇×#36762, …
maximal normal subgroup of	C₃₇×#12143, C₃₇×#12237, C₃₇×#36762, …
maximal quotient of	C₃₇×#14400, C₃₇×#14432, C₃₇×#14462, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1521);

C37×#2789 #17991607