C₃₇×#1400 #17990218

order	4736
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#1400

Subgroups

	subgroup	G/H
center	C₈×C₃₇	C₂²⋊C₄
commutator	C₂²	C₂×C₁₆×C₃₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₃₇
socle	C₂×C₃₇	C₂²⋊C₁₆
prime radical	C₂³×C₃₇	C₁₆
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₃₇ ◁ C₂×C₁₆×C₃₇ ◁ G

74 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(38,39,40,45,41,46,49,57,42,47,50,58,51,59,62,67,43,44,48,54,52,55,60,64,53,56,61,65,63,66,68,69);(39,44)(40,48)(46,55)(47,56)(49,60)(50,61)(59,66)(62,68)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#7336, C₃₇×#7337, C₃₇×#7364, …
maximal normal subgroup of	C₃₇×#7336, C₃₇×#7337, C₃₇×#7364, …
maximal quotient of	C₃₇×#7334, C₃₇×#7362, C₃₇×#7380, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 132);

C37×#1400 #17990218