D₉₃₆₇ #34035488

order	18734
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₃₆₇
unambiguous semidirect product	C₁₇⋊D₅₅₁
unambiguous semidirect product	C₁₉⋊D₄₉₃
unambiguous semidirect product	C₂₉⋊D₃₂₃

Splittings

Fitting, socle, derived, Hall	C₁₇×C₁₉×C₂₉ ⋊ C₂
Hall	C₁₉×C₂₉ ⋊ D₁₇
Hall	C₁₇×C₂₉ ⋊ D₁₉
Hall	C₁₇×C₁₉ ⋊ D₂₉
Sylow	C₂₉ ⋊ D₃₂₃
Sylow	C₁₉ ⋊ D₄₉₃
Sylow	C₁₇ ⋊ D₅₅₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₁₉×C₂₉	C₂
LCS	G ▷ C₁₇×C₁₉×C₂₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 9367

A minimal faithful permutation representation — 2 generators on 65 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)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,36)(20,35)(21,34)(22,33)(23,32)(24,31)(25,30)(26,29)(27,28)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Polycyclic presentation:

2,17,19,29|b^a=b^16,c^a=c^18,d^a=d^28

Conjugacy classes & character table

4685 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₉×D₃₂₃, D₁₉×D₄₉₃, D₁₇×D₅₅₁, …
maximal normal subgroup of	D₂₉×D₃₂₃, D₁₉×D₄₉₃, D₁₇×D₅₅₁, …
maximal quotient of	Dic₉₃₆₇, C₂×D₉₃₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18734, 8);

D9367 #34035488