D₉₈₆₇ #34089412

order	19734
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₈₆₇
unambiguous semidirect product	C₃⋊D₃₂₈₉
unambiguous semidirect product	C₁₁⋊D₈₉₇
unambiguous semidirect product	C₁₃⋊D₇₅₉
unambiguous semidirect product	C₂₃⋊D₄₂₉

Splittings

Fitting, socle, derived, Hall	C₃×C₁₁×C₁₃×C₂₃ ⋊ C₂
Hall	C₁₁×C₁₃×C₂₃ ⋊ D₃
Hall	C₃×C₁₃×C₂₃ ⋊ D₁₁
Hall	C₃×C₁₁×C₂₃ ⋊ D₁₃
Hall	C₃×C₁₁×C₁₃ ⋊ D₂₃
Hall	C₁₃×C₂₃ ⋊ D₃₃
Hall	C₁₁×C₂₃ ⋊ D₃₉
Hall	C₁₁×C₁₃ ⋊ D₆₉
Hall	C₃×C₂₃ ⋊ D₁₄₃
Hall	C₃×C₁₃ ⋊ D₂₅₃
Hall	C₃×C₁₁ ⋊ D₂₉₉
Sylow	C₂₃ ⋊ D₄₂₉
Sylow	C₁₃ ⋊ D₇₅₉
Sylow	C₁₁ ⋊ D₈₉₇
Sylow	C₃ ⋊ D₃₂₈₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₁₃×C₂₃	C₂
LCS	G ▷ C₃×C₁₁×C₁₃×C₂₃
UCS	C₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 9867

A minimal faithful permutation representation — 2 generators on 50 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)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50);(2,3)(5,14)(6,13)(7,12)(8,11)(9,10)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,50)(30,49)(31,48)(32,47)(33,46)(34,45)(35,44)(36,43)(37,42)(38,41)(39,40)

Polycyclic presentation:

2,3,11,13,23|b^a=b^2,c^a=c^10,d^a=d^12,e^a=e^22

Conjugacy classes & character table

4935 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₉₆₀₁
maximal quotient of	D₂₉₆₀₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19734, 19);

D9867 #34089412