C₃×C₁₉×D₁₇ #14515580

order	1938
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₁₉×D₁₇
unambiguous semidirect product	C₁₇⋊(C₂×C₃×C₁₉)

Splittings

Fitting, socle, Hall	C₃×C₁₇×C₁₉ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₃×C₁₉
Hall	C₁₇×C₁₉ ⋊ C₂×C₃
Hall	C₃×C₁₇ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₁₉	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃×C₁₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 969

A minimal faithful permutation representation — 2 generators on 39 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);(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₁₉×#595, C₃×C₁₉⋊#595, C₃×D₁₇×D₁₉, …
maximal normal subgroup of	C₃×C₁₉×#595, C₃×C₁₉⋊#595, C₃×D₁₇×D₁₉, …
maximal quotient of	C₃×C₁₉×Dic₁₇, C₂×C₃×C₁₉×D₁₇, C₃×C₇×C₁₉×D₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1938, 6);

C3×C19×D17 #14515580