C₃₇×#352 #14557017

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

Aliases

direct product

C₃₇×#352

Subgroups

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

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 592

A minimal faithful permutation representation — 2 generators on 53 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)(40,46)(41,49,50,44)(42,45)(43,47,51,53)(48,52);(38,40,42,48)(39,43,45,51)(41,47,50,53)(44,46,49,52)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₃₇×#352, C₃₇×#2120, C₃₇×#2121, …
maximal normal subgroup of	C₂×C₃₇×#352, C₃₇×#2120, C₃₇×#2121, …
maximal quotient of	C₃₇×#1317, C₃₇×#1326, C₃₇×#1344, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 33);

C37×#352 #14557017

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₃₇×#352 #14557017