D₁₇×C₆₁ #14523409

order	2074
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₆₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₇×C₆₁
unambiguous semidirect product	C₁₇⋊(C₂×C₆₁)

Splittings

Fitting, socle, Hall	C₁₇×C₆₁ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₆₁

Subgroups

	subgroup	G/H
center, hypercenter	C₆₁	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₆₁
Frattini	C₁	G
Fitting, socle	C₁₇×C₆₁	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₆₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 78
transitive degree	μ_t(G) = 1037

A minimal faithful permutation representation — 2 generators on 78 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₆₁×#595, #16861897, D₁₇×D₆₁, …
maximal normal subgroup of	C₆₁×#595, #16861897, D₁₇×D₆₁, …
maximal quotient of	C₆₁×Dic₁₇, C₂×D₁₇×C₆₁, C₇×D₁₇×C₆₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2074, 1);

D17×C61 #14523409