C₃₇×#2222 #17991040

order	4736
nilpotency class	4
isoclinism	isoclinic class of #2221
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#2222

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	#466
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃₇
prime radical	#41×C₃₇	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂×C₄×C₃₇ ◁ #131×C₃₇ ◁ G

140 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 101
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 3 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)(38,39,45,51)(40,52,58,80)(41,59,62,76)(42,63,65,74)(43,50,44,49)(46,67,71,55)(47,66,73,61)(48,64,75,53)(54,83,86,100)(56,79,57,78)(60,91,92,72)(68,95,96,101)(69,87,70,81)(77,88,99,85)(82,90,93,98)(84,89,94,97);(38,40,53,81,44,57,65,67,45,58,64,87,43,56,42,55)(39,46,63,79,50,70,75,80,51,71,74,78,49,69,48,52)(41,54,82,101,61,85,92,94,62,86,93,95,66,88,60,84)(47,68,90,83,59,89,91,99,73,96,98,100,76,97,72,77);(38,41)(39,47)(40,54)(42,60)(43,66)(44,61)(45,62)(46,68)(48,72)(49,76)(50,59)(51,73)(52,77)(53,82)(55,84)(56,88)(57,85)(58,86)(63,90)(64,93)(65,92)(67,94)(69,97)(70,89)(71,96)(74,98)(75,91)(78,100)(79,83)(80,99)(81,101)(87,95)

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃₇×#13671, C₃₇×#13672, C₃₇×#13701, …
maximal normal subgroup of	C₃₇×#13671, C₃₇×#13672, C₃₇×#13701, …
maximal quotient of	C₃₇×#12431, C₃₇×#12434, C₃₇×#12440, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 954);