C₁₃⋊C₃×C₆₁ #14558649

order	2379
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₆₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃⋊C₃×C₆₁
unambiguous semidirect product	C₁₃⋊(C₃×C₆₁)

Splittings

Fitting, socle, Hall	C₁₃×C₆₁ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₃×C₆₁

Subgroups

	subgroup	G/H
center, hypercenter	C₆₁	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₁₃×C₆₁	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₆₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 74
transitive degree	μ_t(G) = 793

A minimal faithful permutation representation — 2 generators on 74 points:

(2,3,5)(4,7,10)(6,9,8)(11,13,12)(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);(1,2,4,3,6,10,7,11,13,5,8,12,9)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₁₃⋊C₃×C₆₁, C₁₃⋊C₃×D₆₁, C₆₁×D₁₃⋊C₃, …
maximal normal subgroup of	C₂×C₁₃⋊C₃×C₆₁, C₁₃⋊C₃×D₆₁, C₆₁×D₁₃⋊C₃, …
maximal quotient of	C₂×C₁₃⋊C₃×C₆₁, C₅×C₁₃⋊C₃×C₆₁, C₇×C₁₃⋊C₃×C₆₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2379, 1);

C13⋊C3×C61 #14558649