C₃₇×#1401 #17990219

order	4736
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#1401

Subgroups

	subgroup	G/H
center	C₁₆×C₃₇	D₄
commutator	C₄	C₂×C₁₆×C₃₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₃₇
socle	C₂×C₃₇	C₂²⋊C₁₆
prime radical	#41×C₃₇	C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₃₇ ◁ C₂×C₁₆×C₃₇ ◁ G

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 2 generators on 101 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)(38,39,42,48,43,49,61,74,44,50,62,75,64,77,89,97,45,51,63,76,65,78,90,98,41,47,58,71,59,72,86,95)(40,52,54,79,55,80,83,99,53,69,81,73,82,93,100,96,56,70,60,87,84,94,88,101,57,46,66,67,85,68,91,92);(38,40)(39,46)(41,57)(42,60)(43,55)(44,53)(45,56)(47,70)(48,73)(49,68)(50,52)(51,69)(54,63)(58,81)(59,85)(61,88)(62,66)(64,82)(65,84)(67,76)(71,79)(72,94)(74,96)(75,87)(77,80)(78,93)(83,90)(86,100)(89,91)(92,98)(95,99)(97,101)

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₃₇×#1401, C₃₇×#13558, C₃₇×#13647, …
maximal normal subgroup of	C₂×C₃₇×#1401, C₃₇×#13558, C₃₇×#13647, …
maximal quotient of	C₃₇×#7335, C₃₇×#7363, C₃₇×D₄⋊C₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 133);

C37×#1401 #17990219