C₃₇×#1408 #17990226

order	4736
nilpotency class	5
isoclinism	isoclinic class of #1408
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₃₇×#1408

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	#353
commutator	C₄²	C₂×C₄×C₃₇
Frattini, cosocle	#127	C₂²×C₃₇
prime radical	C₃₇×#493	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×C₃₇ ◁ C₂×C₄×C₃₇ ◁ #127×C₃₇ ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 592

A minimal faithful permutation representation — 2 generators on 53 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)(40,47,48,43)(41,45,51,44)(42,46)(49,52,50,53);(38,40)(39,43)(41,50)(42,49)(44,52)(45,47)(46,53)(48,51)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃₇×#7515, C₃₇×#7516, C₃₇×#7529, …
maximal normal subgroup of	C₃₇×#7515, C₃₇×#7516, C₃₇×#7529, …
maximal quotient of	C₃₇×#7354, C₃₇×#7370, C₃₇×#7402, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 140);

C37×#1408 #17990226

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₃₇×#1408 #17990226