C₃×C₅₉⋊C₈ #13083456

order	1416
isoclinism	isoclinic class of D₅₉
automorphism	?
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₅₉⋊C₈
unambiguous semidirect product	C₅₉⋊(C₃×C₈)

Splittings

derived, Sylow	C₅₉ ⋊ C₃×C₈
Hall	C₃×C₅₉ ⋊ C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄	D₅₉
commutator, hypocenter	C₅₉	C₃×C₈
Frattini	C₄	C₃×D₅₉
Fitting	C₃×C₄×C₅₉	C₂
socle, prime radical	C₂×C₃×C₅₉	C₄
cosocle	C₄×C₅₉	C₂×C₃
LCS	G ▷ C₅₉
UCS	C₁ ◁ C₃×C₄

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 70
transitive degree	μ_t(G) = 1416

A minimal faithful permutation representation — 2 generators on 70 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1416, 2);

C3×C59⋊C8 #13083456