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C₃₇×AΣL(1,𝔽₁₆) #14557016

order	2368
nilpotency class	4
isoclinism	isoclinic class of AΣL(1,𝔽₁₆)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₃₇ · Schur multiplier (H₂) = C₂²

Aliases

C₃₇×AΣL(1,𝔽₁₆)

Subgroups

	subgroup	G/H
center, socle	C₂×C₃₇	#99
commutator	C₂³	C₂×C₄×C₃₇
Frattini, cosocle	C₂×D₄	C₂²×C₃₇
prime radical	#120×C₃₇	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₇ ◁ C₂²×C₃₇ ◁ C₂×D₄×C₃₇ ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 296

A minimal faithful permutation representation — 2 generators on 45 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);(39,42)(43,44)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₃₇×AΣL(1,𝔽₁₆), C₃₇×#2120, C₃₇×#2121, …
maximal normal subgroup of	C₂×C₃₇×AΣL(1,𝔽₁₆), C₃₇×#2120, C₃₇×#2121, …
maximal quotient of	C₃₇×#1316, C₃₇×#1326, C₃₇×#1343, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 32);