D₁₆₁₉₅ #44569258

order	32390
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₁₉₅
unambiguous semidirect product	C₅⋊D₃₂₃₉
unambiguous semidirect product	C₄₁⋊D₃₉₅
unambiguous semidirect product	C₇₉⋊D₂₀₅

Splittings

Fitting, socle, derived, Hall	C₅×C₄₁×C₇₉ ⋊ C₂
Hall	C₄₁×C₇₉ ⋊ D₅
Hall	C₅×C₇₉ ⋊ D₄₁
Hall	C₅×C₄₁ ⋊ D₇₉
Sylow	C₇₉ ⋊ D₂₀₅
Sylow	C₄₁ ⋊ D₃₉₅
Sylow	C₅ ⋊ D₃₂₃₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₄₁×C₇₉	C₂
LCS	G ▷ C₅×C₄₁×C₇₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 16195

A minimal faithful permutation representation — 2 generators on 125 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)(47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125);(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)(48,125)(49,124)(50,123)(51,122)(52,121)(53,120)(54,119)(55,118)(56,117)(57,116)(58,115)(59,114)(60,113)(61,112)(62,111)(63,110)(64,109)(65,108)(66,107)(67,106)(68,105)(69,104)(70,103)(71,102)(72,101)(73,100)(74,99)(75,98)(76,97)(77,96)(78,95)(79,94)(80,93)(81,92)(82,91)(83,90)(84,89)(85,88)(86,87)

Polycyclic presentation:

2,5,41,79|b^a=b^4,c^a=c^40,d^a=d^78

Conjugacy classes & character table

8099 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₆₁₉₅
maximal normal subgroup of	C₂×D₁₆₁₉₅
maximal quotient of	Dic₁₆₁₉₅, C₂×D₁₆₁₉₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32390, 9);

D16195 #44569258