C₃×D₃×C₁₇×C₄₃ #27190495

order	13158
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₇×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₃×C₁₇×C₄₃
unambiguous semidirect product	C₃⋊(C₂×C₃×C₁₇×C₄₃)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇×C₄₃	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃×C₁₇×C₄₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₄₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₁₇×C₄₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 4386

A minimal faithful permutation representation — 2 generators on 66 points:

(1,2,3)(5,6)(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49)(50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(4,5,6)

Conjugacy classes & character table

6579 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₃×C₁₇×D₄₃, C₃×D₃×D₁₇×C₄₃, C₃×D₃×D₇₃₁, …
maximal normal subgroup of	C₃×D₃×C₁₇×D₄₃, C₃×D₃×D₁₇×C₄₃, C₃×D₃×D₇₃₁, …
maximal quotient of	C₃×Dic₃×C₁₇×C₄₃, C₂×C₃×D₃×C₁₇×C₄₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13158, 29);

C3×D3×C17×C43 #27190495