C₃×#66491 #11758288

order	984
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₃×C₈ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×#66491

Splittings

derived, Sylow	C₄₁ ⋊ C₃×C₈
Hall	C₃×C₄₁ ⋊ C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄	D₄₁
commutator, hypocenter	C₄₁	C₃×C₈
Frattini	C₄	C₃×D₄₁
Fitting	C₃×C₄×C₄₁	C₂
socle, prime radical	C₂×C₃×C₄₁	C₄
cosocle	C₄×C₄₁	C₂×C₃
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₃×C₄

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 52
transitive degree	μ_t(G) = 984

A minimal faithful permutation representation — 2 generators on 52 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)(45,46,47,49,48,50,51,52);(4,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,44,42,40,38,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8,6)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×#10620270, C₃⋊#10620270, D₃×#66491, …
maximal normal subgroup of	C₃×#10620270, C₃⋊#10620270, D₃×#66491, …
maximal quotient of	C₃×#10620268, C₂×C₃×#66491

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(984, 2);

C3×#66491 #11758288