C₁₇×D₁₄₁ #18012369

order	4794
isoclinism	isoclinic class of D₁₄₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₁₄₁
unambiguous semidirect product	C₃⋊(C₁₇×D₄₇)
unambiguous semidirect product	C₄₇⋊(D₃×C₁₇)

Splittings

Fitting, socle, Hall	C₃×C₁₇×C₄₇ ⋊ C₂
derived, Hall	C₃×C₄₇ ⋊ C₂×C₁₇
Hall	C₁₇×C₄₇ ⋊ D₃
Hall	C₃×C₁₇ ⋊ D₄₇
Sylow	C₄₇ ⋊ D₃×C₁₇
Sylow	C₃ ⋊ C₁₇×D₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	D₁₄₁
commutator, cosocle, hypocenter	C₃×C₄₇	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₁₇×C₄₇	C₂
LCS	G ▷ C₃×C₄₇
UCS	C₁ ◁ C₁₇

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 2397

A minimal faithful permutation representation — 2 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67);(19,20)(22,67)(23,66)(24,65)(25,64)(26,63)(27,62)(28,61)(29,60)(30,59)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)

Conjugacy classes & character table

1224 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₇×D₄₂₃, C₁₇×C₃⋊D₁₄₁, C₃×C₁₇×D₁₄₁, …
maximal normal subgroup of	C₃×C₁₇×D₁₄₁, C₅×C₁₇×D₁₄₁, C₇×C₁₇×D₁₄₁
maximal quotient of	C₁₇×D₄₂₃, C₁₇×C₃⋊D₁₄₁, C₃×C₁₇×D₁₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4794, 6);

C17×D141 #18012369