C₃₇×#2098 #17990916

order	4736
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#2098

Subgroups

	subgroup	G/H
center	C₄×C₃₇	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃₇
socle	C₂×C₃₇	#399
prime radical	C₂×#41×C₃₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₃₇ ◁ C₂²×C₄×C₃₇ ◁ G

210 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 69
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 3 generators on 69 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)(38,39,42,47,43,48,44,58)(40,49,51,61,53,65,52,45)(41,54,56,64,57,46,59,63)(50,66,55,69,67,62,68,60);(38,40,44,51,43,53,42,52)(39,45,58,49,48,61,47,65)(41,55,59,67,57,68,56,50)(46,62,64,60,54,66,63,69);(38,41)(39,46)(40,50)(42,56)(43,57)(44,59)(45,60)(47,63)(48,54)(49,66)(51,55)(52,68)(53,67)(58,64)(61,69)(62,65)

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃₇×#7438, C₃₇×#7439, C₃₇×#12301, …
maximal normal subgroup of	C₃₇×#7438, C₃₇×#7439, C₃₇×#12301, …
maximal quotient of	C₃₇×#10659, C₃₇×#10660, C₃₇×#10661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 830);