C₄₃×C₃⋊D₅₁ #27190489

order	13158
isoclinism	isoclinic class of C₃⋊D₅₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₄₃×C₃⋊D₅₁
unambiguous semidirect product	C₃⋊(C₄₃×D₅₁)
unambiguous semidirect product	C₁₇⋊(C₃⋊D₃×C₄₃)

Splittings

Fitting, socle, Hall	C₃²×C₁₇×C₄₃ ⋊ C₂
derived, Hall	C₃²×C₁₇ ⋊ C₂×C₄₃
Hall	C₁₇×C₄₃ ⋊ C₃⋊D₃
Hall	C₃²×C₄₃ ⋊ D₁₇
Sylow	C₁₇ ⋊ C₃⋊D₃×C₄₃
Sylow	C₃² ⋊ D₁₇×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄₃	C₃⋊D₅₁
commutator, cosocle, hypocenter	C₃²×C₁₇	C₂×C₄₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₄₃	C₂
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₄₃

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 6579

A minimal faithful permutation representation — 3 generators on 66 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,20)(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);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(21,22,23);(18,19,20)

Conjugacy classes & character table

3354 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₃×#10597479, C₄₃⋊#10597479, D₃×C₄₃×D₅₁, …
maximal normal subgroup of	C₄₃×#10597479, C₄₃⋊#10597479, D₃×C₄₃×D₅₁, …
maximal quotient of	C₄₃×C₃⋊Dic₅₁, C₂×C₄₃×C₃⋊D₅₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13158, 23);

C43×C3⋊D51 #27190489