D₉₄₄₃ #34038522

order	18886
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₄₄₃
unambiguous semidirect product	C₇⋊D₁₃₄₉
unambiguous semidirect product	C₁₉⋊D₄₉₇
unambiguous semidirect product	C₇₁⋊D₁₃₃

Splittings

Fitting, socle, derived, Hall	C₇×C₁₉×C₇₁ ⋊ C₂
Hall	C₁₉×C₇₁ ⋊ D₇
Hall	C₇×C₇₁ ⋊ D₁₉
Hall	C₇×C₁₉ ⋊ D₇₁
Sylow	C₇₁ ⋊ D₁₃₃
Sylow	C₁₉ ⋊ D₄₉₇
Sylow	C₇ ⋊ D₁₃₄₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₉×C₇₁	C₂
LCS	G ▷ C₇×C₁₉×C₇₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 9443

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

Polycyclic presentation:

2,7,19,71|b^a=b^6,c^a=c^18,d^a=d^70

Conjugacy classes & character table

4723 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇₁×D₁₃₃, D₁₉×D₄₉₇, D₇×D₁₃₄₉, …
maximal normal subgroup of	D₇₁×D₁₃₃, D₁₉×D₄₉₇, D₇×D₁₃₄₉, …
maximal quotient of	Dic₉₄₄₃, C₂×D₉₄₄₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18886, 9);

D9443 #34038522