C₃₇×#2884 #17991702

order	4736
nilpotency class	3
isoclinism	isoclinic class of #2883
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₃₇×#2884

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₃₇
Frattini, cosocle	C₂³	C₂⁴×C₃₇
prime radical	C₂×2₋¹⁺⁴×C₃₇	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×Q₈×C₃₇ ◁ G

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 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)(40,48,51,44)(41,45)(42,46)(43,47)(49,62,65,56)(50,63,67,57)(52,58)(53,59)(54,60)(55,61)(64,69,66,68);(38,40)(39,44)(41,49)(42,50)(43,51)(45,56)(46,57)(47,48)(52,64)(53,65)(54,66)(55,67)(58,68)(59,62)(60,69)(61,63);(38,41,43,53)(39,45,47,59)(40,49,51,65)(42,54,55,52)(44,56,48,62)(46,60,61,58)(50,66,67,64)(57,69,63,68);(38,42,43,55)(39,46,47,61)(40,50,51,67)(41,52,53,54)(44,57,48,63)(45,58,59,60)(49,64,65,66)(56,68,62,69)

Conjugacy classes & character table

1517 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#13101, C₃₇×#13103, C₃₇×#21783, …
maximal normal subgroup of	C₃₇×#13101, C₃₇×#13103, C₃₇×#21783, …
maximal quotient of	C₃₇×#17352, C₃₇×#17353, C₃₇×#17371, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1616);

C37×#2884 #17991702