D₁₄₉₁₁ #44447299

order	29822
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₄₉₁₁
unambiguous semidirect product	C₁₃⋊D₁₁₄₇
unambiguous semidirect product	C₃₁⋊D₄₈₁
unambiguous semidirect product	C₃₇⋊D₄₀₃

Splittings

Fitting, socle, derived, Hall	C₁₃×C₃₁×C₃₇ ⋊ C₂
Hall	C₃₁×C₃₇ ⋊ D₁₃
Hall	C₁₃×C₃₇ ⋊ D₃₁
Hall	C₁₃×C₃₁ ⋊ D₃₇
Sylow	C₃₇ ⋊ D₄₀₃
Sylow	C₃₁ ⋊ D₄₈₁
Sylow	C₁₃ ⋊ D₁₁₄₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₃₁×C₃₇	C₂
LCS	G ▷ C₁₃×C₃₁×C₃₇
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 14911

A minimal faithful permutation representation — 2 generators on 81 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,44)(16,43)(17,42)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(46,81)(47,80)(48,79)(49,78)(50,77)(51,76)(52,75)(53,74)(54,73)(55,72)(56,71)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)

Polycyclic presentation:

2,13,31,37|b^a=b^12,c^a=c^30,d^a=d^36

Conjugacy classes & character table

7457 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₄₉₁₁
maximal normal subgroup of	C₂×D₁₄₉₁₁
maximal quotient of	Dic₁₄₉₁₁, C₂×D₁₄₉₁₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29822, 8);

D14911 #44447299