C₂×C₁₃⋊C₃×C₄₃ #16809797

order	3354
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₃⋊C₃×C₄₃
unambiguous semidirect product	(C₂×C₁₃)⋊(C₃×C₄₃)

Splittings

Fitting, socle, Hall	C₂×C₁₃×C₄₃ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₂×C₃×C₄₃
Hall	C₁₃×C₄₃ ⋊ C₂×C₃
Hall	C₂×C₁₃ ⋊ C₃×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₃	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₄₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₄₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₄₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 1118

A minimal faithful permutation representation — 2 generators on 58 points:

(1,2)(4,5,7)(6,9,12)(8,11,10)(13,15,14)(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);(3,4,6,5,8,12,9,13,15,7,10,14,11)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₅×C₁₃⋊C₃×C₄₃, D₅×C₁₃⋊C₃×C₄₃, C₂×C₇×C₁₃⋊C₃×C₄₃, …
maximal normal subgroup of	C₂×C₅×C₁₃⋊C₃×C₄₃, C₂×C₇×C₁₃⋊C₃×C₄₃, C₂×C₁₃⋊C₃×C₄₃⋊C₇, …
maximal quotient of	C₂×C₅×C₁₃⋊C₃×C₄₃, D₅×C₁₃⋊C₃×C₄₃, C₂×C₇×C₁₃⋊C₃×C₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3354, 3);

C2×C13⋊C3×C43 #16809797