D₁₂₀₉₅ #37564064

order	24190
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₀₉₅
unambiguous semidirect product	C₅⋊D₂₄₁₉
unambiguous semidirect product	C₄₁⋊D₂₉₅
unambiguous semidirect product	C₅₉⋊D₂₀₅

Splittings

Fitting, socle, derived, Hall	C₅×C₄₁×C₅₉ ⋊ C₂
Hall	C₄₁×C₅₉ ⋊ D₅
Hall	C₅×C₅₉ ⋊ D₄₁
Hall	C₅×C₄₁ ⋊ D₅₉
Sylow	C₅₉ ⋊ D₂₀₅
Sylow	C₄₁ ⋊ D₂₉₅
Sylow	C₅ ⋊ D₂₄₁₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₄₁×C₅₉	C₂
LCS	G ▷ C₅×C₄₁×C₅₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 105
transitive degree	μ_t(G) = 12095

A minimal faithful permutation representation — 2 generators on 105 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);(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)(48,105)(49,104)(50,103)(51,102)(52,101)(53,100)(54,99)(55,98)(56,97)(57,96)(58,95)(59,94)(60,93)(61,92)(62,91)(63,90)(64,89)(65,88)(66,87)(67,86)(68,85)(69,84)(70,83)(71,82)(72,81)(73,80)(74,79)(75,78)(76,77)

Polycyclic presentation:

2,5,41,59|b^a=b^4,c^a=c^40,d^a=d^58

Conjugacy classes & character table

6049 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24190, 9);

D12095 #37564064