C₃₇×#1323 #17990141

order	4736
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃₇×#1323

Subgroups

	subgroup	G/H
center	C₂×C₄×C₃₇	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₈×C₃₇
Frattini, cosocle	C₂²×C₈	C₂²×C₃₇
socle	C₂²×C₃₇	C₂²⋊C₈
prime radical	C₂³×C₃₇	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₂²×C₈×C₃₇ ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 2368

A minimal faithful permutation representation — 2 generators on 77 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)(40,44,45,42)(41,43)(46,47,50,55,51,56,65,73,52,57,66,74,49,54,63,71)(48,58,60,75,59,69,76,72,61,70,64,77,62,53,67,68);(38,40,41,45)(39,42,43,44)(46,48)(47,53)(49,62)(50,64)(51,59)(52,61)(54,70)(55,72)(56,58)(57,69)(60,66)(63,76)(65,67)(68,74)(71,75)(73,77)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃₇×#1323, C₃₇×#11443, C₃₇×#11444, …
maximal normal subgroup of	C₂×C₃₇×#1323, C₃₇×#11443, C₃₇×#11444, …
maximal quotient of	C₃₇×#7065, C₃₇×#7066, C₃₇×#7067, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 55);

C37×#1323 #17990141