C₃₇×(C₃⋊D₃)⋊C₃ #14522006

order	1998
isoclinism	isoclinic class of (C₃⋊D₃)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₃₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃₇×(C₃⋊D₃)⋊C₃
unambiguous semidirect product	(C₃⋊D₃)⋊(C₃×C₃₇)

Splittings

Fitting, Hall	H(3,𝔽₃)×C₃₇ ⋊ C₂
derived	C₃² ⋊ C₂×C₃×C₃₇
Sylow	H(3,𝔽₃) ⋊ C₂×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃₇	(C₃⋊D₃)⋊C₃
commutator, cosocle, hypocenter	C₃²	C₂×C₃×C₃₇
Frattini	C₃	C₃×D₃×C₃₇
Fitting	H(3,𝔽₃)×C₃₇	C₂
socle	C₃×C₃₇	C₃×D₃
LCS	G ▷ C₃²
UCS	C₁ ◁ C₃₇

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 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)(39,44,46,41,42,45)(40,43);(38,39,41)(40,42,45)(43,46,44)

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, 36);

C37×(C3⋊D3)⋊C3 #14522006