D₁₃₂₄₃ #40996642

order	26486
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₃₂₄₃
unambiguous semidirect product	C₁₇⋊D₇₇₉
unambiguous semidirect product	C₁₉⋊D₆₉₇
unambiguous semidirect product	C₄₁⋊D₃₂₃

Splittings

Fitting, socle, derived, Hall	C₁₇×C₁₉×C₄₁ ⋊ C₂
Hall	C₁₉×C₄₁ ⋊ D₁₇
Hall	C₁₇×C₄₁ ⋊ D₁₉
Hall	C₁₇×C₁₉ ⋊ D₄₁
Sylow	C₄₁ ⋊ D₃₂₃
Sylow	C₁₉ ⋊ D₆₉₇
Sylow	C₁₇ ⋊ D₇₇₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₁₉×C₄₁	C₂
LCS	G ▷ C₁₇×C₁₉×C₄₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 13243

A minimal faithful permutation representation — 2 generators on 77 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);(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)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58)

Polycyclic presentation:

2,17,19,41|b^a=b^16,c^a=c^18,d^a=d^40

Conjugacy classes & character table

6623 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₃₂₄₃
maximal normal subgroup of	C₂×D₁₃₂₄₃
maximal quotient of	Dic₁₃₂₄₃, C₂×D₁₃₂₄₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26486, 8);

D13243 #40996642