C₃₇×M₁₂₈ #17990246

order	4736
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₂×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×M₁₂₈

Subgroups

	subgroup	G/H
center	C₃₂×C₃₇	C₂²
commutator	C₂	C₂×C₃₂×C₃₇
Frattini, cosocle	C₃₂	C₂²×C₃₇
socle	C₂×C₃₇	C₂×C₃₂
prime radical	C₂²×C₃₇	C₃₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃₂×C₃₇ ◁ G

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

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7511, C₃₇×#7513, C₃₇×#7514, …
maximal normal subgroup of	C₃₇×#7511, C₃₇×#7513, C₃₇×#7514, …
maximal quotient of	C₃₇×#7510, C₃₇×C₂²⋊C₆₄, C₃₇×C₄⋊C₆₄, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 160);

C37×M128 #17990246