C₃₇×#272 #14522013

order	1998
isoclinism	isoclinic class of #272
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×#272

Splittings

Fitting, Hall	H(3,𝔽₃)×C₃₇ ⋊ C₂
derived, Sylow	H(3,𝔽₃) ⋊ C₂×C₃₇

Subgroups

	subgroup	G/H
center, socle, hypercenter	C₃×C₃₇	C₃⋊D₃
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂×C₃₇
Frattini	C₃	C₃⋊D₃×C₃₇
Fitting	H(3,𝔽₃)×C₃₇	C₂
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃×C₃₇

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 333

A minimal faithful permutation representation — 3 generators on 46 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)(39,41)(42,46)(43,45);(39,42,43)(41,45,46);(38,39,41)(40,43,45)(42,46,44)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1998, 43);

C37×#272 #14522013