C₃₇×#519 #14557184

order	2368
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₃₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₃₇×#519

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃₇	C₂⁴
commutator	C₂	C₂³×C₄×C₃₇
Frattini, cosocle	C₂²	C₂⁴×C₃₇
prime radical	C₂³×C₃₇	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₇ ◁ G

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 1184

A minimal faithful permutation representation — 4 generators on 57 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)(38,39,40,41)(43,47)(45,53)(48,50)(51,57);(42,43,46,47)(44,50,52,48)(45,49,53,54)(51,56,57,55);(42,44,46,52)(43,48,47,50)(45,51,53,57)(49,55,54,56);(42,45)(43,49)(44,51)(46,53)(47,54)(48,55)(50,56)(52,57)

Conjugacy classes & character table

1258 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₇×#1830, C₃₇×#1857, C₃₇×#1886, …
maximal normal subgroup of	C₃₇×#1830, C₃₇×#1857, C₃₇×#1886, …
maximal quotient of	C₃₇×#2274, C₃₇×#2276, C₃₇×#2310, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 200);

C37×#519 #14557184