D₇₃₃₇ #28412733

order	14674
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₇₃₃₇
unambiguous semidirect product	C₁₁⋊D₆₆₇
unambiguous semidirect product	C₂₃⋊D₃₁₉
unambiguous semidirect product	C₂₉⋊D₂₅₃

Splittings

Fitting, socle, derived, Hall	C₁₁×C₂₃×C₂₉ ⋊ C₂
Hall	C₂₃×C₂₉ ⋊ D₁₁
Hall	C₁₁×C₂₉ ⋊ D₂₃
Hall	C₁₁×C₂₃ ⋊ D₂₉
Sylow	C₂₉ ⋊ D₂₅₃
Sylow	C₂₃ ⋊ D₃₁₉
Sylow	C₁₁ ⋊ D₆₆₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₂₃×C₂₉	C₂
LCS	G ▷ C₁₁×C₂₃×C₂₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 7337

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

Polycyclic presentation:

2,11,23,29|b^a=b^10,c^a=c^22,d^a=d^28

Conjugacy classes & character table

3670 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₉×D₂₅₃, D₂₃×D₃₁₉, D₁₁×D₆₆₇, …
maximal normal subgroup of	D₂₉×D₂₅₃, D₂₃×D₃₁₉, D₁₁×D₆₆₇, …
maximal quotient of	Dic₇₃₃₇, C₂×D₇₃₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14674, 9);

D7337 #28412733