C₁₇×D₅₇ #14515583

order	1938
isoclinism	isoclinic class of D₅₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₅₇
unambiguous semidirect product	C₃⋊(C₁₇×D₁₉)
unambiguous semidirect product	C₁₉⋊(D₃×C₁₇)

Splittings

Fitting, socle, Hall	C₃×C₁₇×C₁₉ ⋊ C₂
derived, Hall	C₃×C₁₉ ⋊ C₂×C₁₇
Hall	C₁₇×C₁₉ ⋊ D₃
Hall	C₃×C₁₇ ⋊ D₁₉
Sylow	C₁₉ ⋊ D₃×C₁₇
Sylow	C₃ ⋊ C₁₇×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	D₅₇
commutator, cosocle, hypocenter	C₃×C₁₉	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₁₉	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₁₇

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);(19,20)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×C₁₇×D₁₉, D₁₇×D₅₇, D₅₁⋊D₁₉, …
maximal normal subgroup of	D₃×C₁₇×D₁₉, D₁₇×D₅₇, D₅₁⋊D₁₉, …
maximal quotient of	C₁₇×Dic₅₇, C₂×C₁₇×D₅₇, C₇×C₁₇×D₅₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1938, 9);

C17×D57 #14515583