D₁₃₄₈₁ #41004050

order	26962
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₃₄₈₁
unambiguous semidirect product	C₁₃⋊D₁₀₃₇
unambiguous semidirect product	C₁₇⋊D₇₉₃
unambiguous semidirect product	C₆₁⋊D₂₂₁

Splittings

Fitting, socle, derived, Hall	C₁₃×C₁₇×C₆₁ ⋊ C₂
Hall	C₁₇×C₆₁ ⋊ D₁₃
Hall	C₁₃×C₆₁ ⋊ D₁₇
Hall	C₁₃×C₁₇ ⋊ D₆₁
Sylow	C₆₁ ⋊ D₂₂₁
Sylow	C₁₇ ⋊ D₇₉₃
Sylow	C₁₃ ⋊ D₁₀₃₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₇×C₆₁	C₂
LCS	G ▷ C₁₃×C₁₇×C₆₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 13481

A minimal faithful permutation representation — 2 generators on 91 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(32,91)(33,90)(34,89)(35,88)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)

Polycyclic presentation:

2,13,17,61|b^a=b^12,c^a=c^16,d^a=d^60

Conjugacy classes & character table

6742 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₃₄₈₁
maximal normal subgroup of	C₂×D₁₃₄₈₁
maximal quotient of	Dic₁₃₄₈₁, C₂×D₁₃₄₈₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26962, 8);

D13481 #41004050