C₁₇×D₄₇ #13097644

order	1598
isoclinism	isoclinic class of D₄₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₄₇
unambiguous semidirect product	C₄₇⋊(C₂×C₁₇)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	D₄₇
commutator, cosocle, hypocenter	C₄₇	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₇×C₄₇	C₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₁₇

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);(19,64)(20,63)(21,62)(22,61)(23,60)(24,59)(25,58)(26,57)(27,56)(28,55)(29,54)(30,53)(31,52)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₁₇×D₄₇, C₂×C₁₇×D₄₇, C₃×C₁₇×D₄₇, …
maximal normal subgroup of	D₁₇×D₄₇, C₂×C₁₇×D₄₇, C₃×C₁₇×D₄₇, …
maximal quotient of	C₁₇×Dic₄₇, C₂×C₁₇×D₄₇, C₃×C₁₇×D₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1598, 2);

C17×D47 #13097644