C₄₃×D₁₅₃ #27190474

order	13158
isoclinism	isoclinic class of D₁₅₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₃×D₁₅₃
unambiguous semidirect product	C₉⋊(D₁₇×C₄₃)
unambiguous semidirect product	C₁₇⋊(D₉×C₄₃)

Splittings

Fitting, Hall	C₉×C₁₇×C₄₃ ⋊ C₂
derived, Hall	C₉×C₁₇ ⋊ C₂×C₄₃
Hall	C₁₇×C₄₃ ⋊ D₉
Hall	C₉×C₄₃ ⋊ D₁₇
Sylow	C₁₇ ⋊ D₉×C₄₃
Sylow	C₉ ⋊ D₁₇×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄₃	D₁₅₃
commutator, cosocle, hypocenter	C₉×C₁₇	C₂×C₄₃
Frattini	C₃	C₄₃×D₅₁
Fitting	C₉×C₁₇×C₄₃	C₂
socle	C₃×C₁₇×C₄₃	D₃
LCS	G ▷ C₉×C₁₇
UCS	C₁ ◁ 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:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(19,21)(20,24)(22,23)(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);(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(18,26,21,24,23,22,20,19,25)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₄₃×D₁₅₃, D₉×D₁₇×C₄₃, D₁₅₃⋊D₄₃, …
maximal normal subgroup of	D₄₃×D₁₅₃, D₉×D₁₇×C₄₃, D₁₅₃⋊D₄₃, …
maximal quotient of	C₄₃×Dic₁₅₃, C₂×C₄₃×D₁₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13158, 8);

C43×D153 #27190474