D₁₁₇₈₁ #37555623

order	23562
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₇₈₁
unambiguous semidirect product	C₇⋊D₁₆₈₃
unambiguous semidirect product	C₉⋊D₁₃₀₉
unambiguous semidirect product	C₁₁⋊D₁₀₇₁
unambiguous semidirect product	C₁₇⋊D₆₉₃

Splittings

Fitting, derived, Hall	C₇×C₉×C₁₁×C₁₇ ⋊ C₂
Hall	C₉×C₁₁×C₁₇ ⋊ D₇
Hall	C₇×C₁₁×C₁₇ ⋊ D₉
Hall	C₇×C₉×C₁₇ ⋊ D₁₁
Hall	C₇×C₉×C₁₁ ⋊ D₁₇
Hall	C₁₁×C₁₇ ⋊ D₆₃
Hall	C₉×C₁₇ ⋊ D₇₇
Hall	C₇×C₁₇ ⋊ D₉₉
Hall	C₉×C₁₁ ⋊ D₁₁₉
Hall	C₇×C₁₁ ⋊ D₁₅₃
Hall	C₇×C₉ ⋊ D₁₈₇
Sylow	C₁₇ ⋊ D₆₉₃
Sylow	C₁₁ ⋊ D₁₀₇₁
Sylow	C₉ ⋊ D₁₃₀₉
Sylow	C₇ ⋊ D₁₆₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₇×C₉×C₁₁×C₁₇	C₂
Frattini	C₃	D₃₉₂₇
socle	C₃×C₇×C₁₁×C₁₇	D₃
LCS	G ▷ C₇×C₉×C₁₁×C₁₇
UCS	C₁

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 44
transitive degree	μ_t(G) = 11781

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3,4,5,6,7,8,9)(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);(2,9)(3,8)(4,7)(5,6)(11,16)(12,15)(13,14)(18,27)(19,26)(20,25)(21,24)(22,23)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Polycyclic presentation:

2,3,7,11,17,3|b^3=f^2,b^a=b^2f,c^a=c^6,d^a=d^10,e^a=e^16,f^a=f^2

Conjugacy classes & character table

5892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 17);

D11781 #37555623