C₆₇×Dic₁₇ #17986932

order	4556
isoclinism	isoclinic class of D₁₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₆₇×Dic₁₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₆₇	D₁₇
commutator, hypocenter	C₁₇	C₄×C₆₇
Frattini	C₂	D₁₇×C₆₇
Fitting, socle, prime radical	C₂×C₁₇×C₆₇	C₂
cosocle	C₂×C₁₇	C₂×C₆₇
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₆₇

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);(68,70,69,71)(73,88)(74,87)(75,86)(76,85)(77,84)(78,83)(79,82)(80,81)

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₆₇×Dic₁₇, C₆₇×Dic₅₁, Dic₁₇×C₆₇⋊C₃, …
maximal normal subgroup of	C₃×C₆₇×Dic₁₇, Dic₁₇×C₆₇⋊C₃, C₅×C₆₇×Dic₁₇, …
maximal quotient of	C₃×C₆₇×Dic₁₇, C₆₇×Dic₅₁, C₅×C₆₇×Dic₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4556, 2);

C67×Dic17 #17986932