C₃₇×#1669 #17990487

order	4736
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1669

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	#121
commutator, Frattini, cosocle	C₄²	C₂³×C₃₇
prime radical	C₂×D₄×C₃₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ C₄²×C₃₇ ◁ G

172 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(40,42)(41,44)(43,45)(46,47,50,53)(48,54,57,61)(49,58,55,52)(51,59,60,56);(46,48,55,59,50,57,49,56)(47,51,58,61,53,60,52,54);(39,42)(40,45)(43,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃₇×#12320, C₃₇×#12321, C₃₇×#12322, …
maximal normal subgroup of	C₃₇×#12320, C₃₇×#12321, C₃₇×#12322, …
maximal quotient of	C₃₇×#8644, C₃₇×#9219, C₃₇×#9561, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 401);