C₂×C₁₃×C₄₃⋊C₃ #16809796

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

Aliases

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

Splittings

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

Subgroups

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

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

Conjugacy classes & character table

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

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3354, 2);

C2×C13×C43⋊C3 #16809796