D₁₇×C₄₁ #13063689

order	1394
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₇×C₄₁
unambiguous semidirect product	C₁₇⋊(C₂×C₄₁)

Splittings

Fitting, socle, Hall	C₁₇×C₄₁ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₄₁	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₄₁
Frattini	C₁	G
Fitting, socle	C₁₇×C₄₁	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₄₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 697

A minimal faithful permutation representation — 2 generators on 58 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);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₁×#595, #14584034, D₁₇×D₄₁, …
maximal normal subgroup of	C₄₁×#595, #14584034, D₁₇×D₄₁, …
maximal quotient of	C₄₁×Dic₁₇, C₂×D₁₇×C₄₁, C₃×D₁₇×C₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1394, 1);

D17×C41 #13063689