C₃₇×#2807 #17991625

order	4736
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₃₇×#2807

Subgroups

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

408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2368

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)(39,42)(40,44)(46,47)(48,52)(49,50)(51,53)(54,55,58,59)(56,60,61,57);(39,42)(43,45)(47,50)(48,53)(55,59)(57,60);(38,39)(40,43)(41,42)(44,45)(46,47)(48,51)(49,50)(52,53)(54,56,58,61)(55,60,59,57);(38,40,41,44)(39,43,42,45)(46,48,49,53)(47,51,50,52)(54,57,58,60)(55,61,59,56)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#12179, C₃₇×#12255, C₃₇×#36748, …
maximal normal subgroup of	C₃₇×#12179, C₃₇×#12255, C₃₇×#36748, …
maximal quotient of	C₃₇×#14442, C₃₇×#14457, C₃₇×#14458, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1539);

C37×#2807 #17991625