C₃₇×#1544 #17990362

order	4736
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₃₇×#1544

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₃₇
Frattini, cosocle	C₄²	C₂³×C₃₇
socle	C₂²×C₃₇	C₂×C₂²⋊C₄
prime radical	C₂³×C₃₇	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂×C₄²×C₃₇ ◁ G

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 2368

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

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#8242, C₃₇×#8244, C₃₇×#8246, …
maximal normal subgroup of	C₃₇×#8242, C₃₇×#8244, C₃₇×#8246, …
maximal quotient of	C₃₇×#7564, C₃₇×#7568, C₃₇×#7646, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 276);

C37×#1544 #17990362