C₁₇×D₉×C₄₃ #27190472

order	13158
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₉×C₄₃
unambiguous semidirect product	C₉⋊(C₂×C₁₇×C₄₃)

Splittings

Fitting, Hall	C₉×C₁₇×C₄₃ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₁₇×C₄₃
Hall	C₉×C₄₃ ⋊ C₂×C₁₇
Hall	C₉×C₁₇ ⋊ C₂×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇×C₄₃	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₁₇×C₄₃
Frattini	C₃	D₃×C₁₇×C₄₃
Fitting	C₉×C₁₇×C₄₃	C₂
socle	C₃×C₁₇×C₄₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₇×C₄₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 6579

A minimal faithful permutation representation — 2 generators on 69 points:

(2,4)(3,7)(5,8)(6,9)(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)(53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69);(1,6,4,3,8,5,7,2,9)

Conjugacy classes & character table

4386 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₇×D₉×D₄₃, D₉×D₁₇×C₄₃, D₉×D₇₃₁, …
maximal normal subgroup of	C₁₇×D₉×D₄₃, D₉×D₁₇×C₄₃, D₉×D₇₃₁, …
maximal quotient of	C₁₇×Dic₉×C₄₃, C₂×C₁₇×D₉×C₄₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13158, 6);

C17×D9×C43 #27190472