D₁₄₀₅₃ #43244602

order	28106
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₄₀₅₃
unambiguous semidirect product	C₁₃⋊D₁₀₈₁
unambiguous semidirect product	C₂₃⋊D₆₁₁
unambiguous semidirect product	C₄₇⋊D₂₉₉

Splittings

Fitting, socle, derived, Hall	C₁₃×C₂₃×C₄₇ ⋊ C₂
Hall	C₂₃×C₄₇ ⋊ D₁₃
Hall	C₁₃×C₄₇ ⋊ D₂₃
Hall	C₁₃×C₂₃ ⋊ D₄₇
Sylow	C₄₇ ⋊ D₂₉₉
Sylow	C₂₃ ⋊ D₆₁₁
Sylow	C₁₃ ⋊ D₁₀₈₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₂₃×C₄₇	C₂
LCS	G ▷ C₁₃×C₂₃×C₄₇
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 14053

A minimal faithful permutation representation — 2 generators on 83 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(38,83)(39,82)(40,81)(41,80)(42,79)(43,78)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)

Polycyclic presentation:

2,13,23,47|b^a=b^12,c^a=c^22,d^a=d^46

Conjugacy classes & character table

7028 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₄₀₅₃
maximal normal subgroup of	C₂×D₁₄₀₅₃
maximal quotient of	Dic₁₄₀₅₃, C₂×D₁₄₀₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28106, 9);

D14053 #43244602