C₁₇×Dic₆₇ #17986933

order	4556
isoclinism	isoclinic class of D₆₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×Dic₆₇
unambiguous semidirect product	C₆₇⋊(C₄×C₁₇)

Splittings

derived, Sylow	C₆₇ ⋊ C₄×C₁₇
Hall	C₁₇×C₆₇ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₆₇
commutator, hypocenter	C₆₇	C₄×C₁₇
Frattini	C₂	C₁₇×D₆₇
Fitting, socle, prime radical	C₂×C₁₇×C₆₇	C₂
cosocle	C₂×C₆₇	C₂×C₁₇
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₂×C₁₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 88
transitive degree	μ_t(G) = 4556

A minimal faithful permutation representation — 2 generators on 88 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88);(18,20,19,21)(23,88)(24,87)(25,86)(26,85)(27,84)(28,83)(29,82)(30,81)(31,80)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,73)(39,72)(40,71)(41,70)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₇×Dic₆₇, C₁₇×Dic₂₀₁, C₁₇×(C₆₇⋊C₃)⋊C₄, …
maximal normal subgroup of	C₃×C₁₇×Dic₆₇, C₁₇×(C₆₇⋊C₃)⋊C₄, C₅×C₁₇×Dic₆₇, …
maximal quotient of	C₃×C₁₇×Dic₆₇, C₁₇×Dic₂₀₁, C₅×C₁₇×Dic₆₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4556, 3);

C17×Dic67 #17986933