D₁₇×C₄₇ #13097643

order	1598
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₇×C₄₇
unambiguous semidirect product	C₁₇⋊(C₂×C₄₇)

Splittings

Fitting, socle, Hall	C₁₇×C₄₇ ⋊ C₂
derived, Sylow	C₁₇ ⋊ C₂×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₄₇	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₄₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₄₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₄₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 64
transitive degree	μ_t(G) = 799

A minimal faithful permutation representation — 2 generators on 64 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);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₇×#595, C₄₇⋊#595, D₁₇×D₄₇, …
maximal normal subgroup of	C₄₇×#595, C₄₇⋊#595, D₁₇×D₄₇, …
maximal quotient of	C₄₇×Dic₁₇, C₂×D₁₇×C₄₇, C₃×D₁₇×C₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1598, 1);

D17×C47 #13097643