D₁₀₁₅₃ #35204572

order	20306
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₀₁₅₃
unambiguous semidirect product	C₁₁⋊D₉₂₃
unambiguous semidirect product	C₁₃⋊D₇₈₁
unambiguous semidirect product	C₇₁⋊D₁₄₃

Splittings

Fitting, socle, derived, Hall	C₁₁×C₁₃×C₇₁ ⋊ C₂
Hall	C₁₃×C₇₁ ⋊ D₁₁
Hall	C₁₁×C₇₁ ⋊ D₁₃
Hall	C₁₁×C₁₃ ⋊ D₇₁
Sylow	C₇₁ ⋊ D₁₄₃
Sylow	C₁₃ ⋊ D₇₈₁
Sylow	C₁₁ ⋊ D₉₂₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₁₃×C₇₁	C₂
LCS	G ▷ C₁₁×C₁₃×C₇₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 10153

A minimal faithful permutation representation — 2 generators on 95 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);(2,11)(3,10)(4,9)(5,8)(6,7)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(26,95)(27,94)(28,93)(29,92)(30,91)(31,90)(32,89)(33,88)(34,87)(35,86)(36,85)(37,84)(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:

2,11,13,71|b^a=b^10,c^a=c^12,d^a=d^70

Conjugacy classes & character table

5078 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20306, 8);

D10153 #35204572