D₁₄₉₆₅ #44471735

order	29930
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₄₉₆₅
unambiguous semidirect product	C₅⋊D₂₉₉₃
unambiguous semidirect product	C₄₁⋊D₃₆₅
unambiguous semidirect product	C₇₃⋊D₂₀₅

Splittings

Fitting, socle, derived, Hall	C₅×C₄₁×C₇₃ ⋊ C₂
Hall	C₄₁×C₇₃ ⋊ D₅
Hall	C₅×C₇₃ ⋊ D₄₁
Hall	C₅×C₄₁ ⋊ D₇₃
Sylow	C₇₃ ⋊ D₂₀₅
Sylow	C₄₁ ⋊ D₃₆₅
Sylow	C₅ ⋊ D₂₉₉₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₄₁×C₇₃	C₂
LCS	G ▷ C₅×C₄₁×C₇₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 119
transitive degree	μ_t(G) = 14965

A minimal faithful permutation representation — 2 generators on 119 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)(47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119);(2,5)(3,4)(7,46)(8,45)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(48,119)(49,118)(50,117)(51,116)(52,115)(53,114)(54,113)(55,112)(56,111)(57,110)(58,109)(59,108)(60,107)(61,106)(62,105)(63,104)(64,103)(65,102)(66,101)(67,100)(68,99)(69,98)(70,97)(71,96)(72,95)(73,94)(74,93)(75,92)(76,91)(77,90)(78,89)(79,88)(80,87)(81,86)(82,85)(83,84)

Polycyclic presentation:

2,5,41,73|b^a=b^4,c^a=c^40,d^a=d^72

Conjugacy classes & character table

7484 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₄₉₆₅
maximal normal subgroup of	C₂×D₁₄₉₆₅
maximal quotient of	Dic₁₄₉₆₅, C₂×D₁₄₉₆₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29930, 9);

D14965 #44471735