D₁₆₉₃₃ #46799694

order	33866
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₉₃₃
unambiguous semidirect product	C₇⋊D₂₄₁₉
unambiguous semidirect product	C₄₁⋊D₄₁₃
unambiguous semidirect product	C₅₉⋊D₂₈₇

Splittings

Fitting, socle, derived, Hall	C₇×C₄₁×C₅₉ ⋊ C₂
Hall	C₄₁×C₅₉ ⋊ D₇
Hall	C₇×C₅₉ ⋊ D₄₁
Hall	C₇×C₄₁ ⋊ D₅₉
Sylow	C₅₉ ⋊ D₂₈₇
Sylow	C₄₁ ⋊ D₄₁₃
Sylow	C₇ ⋊ D₂₄₁₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₄₁×C₅₉	C₂
LCS	G ▷ C₇×C₄₁×C₅₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 107
transitive degree	μ_t(G) = 16933

A minimal faithful permutation representation — 2 generators on 107 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)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(2,7)(3,6)(4,5)(9,48)(10,47)(11,46)(12,45)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(50,107)(51,106)(52,105)(53,104)(54,103)(55,102)(56,101)(57,100)(58,99)(59,98)(60,97)(61,96)(62,95)(63,94)(64,93)(65,92)(66,91)(67,90)(68,89)(69,88)(70,87)(71,86)(72,85)(73,84)(74,83)(75,82)(76,81)(77,80)(78,79)

Polycyclic presentation:

2,7,41,59|b^a=b^6,c^a=c^40,d^a=d^58

Conjugacy classes & character table

8468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33866, 8);

D16933 #46799694