D₂₀₁⋊(C₅⋊D₅) #34117286

order	20100
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₅

Aliases

unambiguous semidirect product

D₂₀₁⋊(C₅⋊D₅)

Splittings

Fitting, socle, derived, Hall	C₃×C₅²×C₆₇ ⋊ C₂²
Hall	C₅²×C₆₇ ⋊ C₂×D₃
Hall	C₃×C₆₇ ⋊ C₂×C₅⋊D₅
Hall	C₃×C₅² ⋊ C₂×D₆₇
Sylow	C₆₇ ⋊ D₃×C₅⋊D₅
Sylow	C₅² ⋊ D₃×D₆₇
Sylow	C₃ ⋊ C₅⋊D₅×D₆₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²×C₆₇	C₂²
LCS	G ▷ C₃×C₅²×C₆₇
UCS	C₁

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 80
transitive degree	μ_t(G) = 5025

A minimal faithful permutation representation — 3 generators on 80 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(69,70)(72,73)(74,75)(76,77)(78,79);(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)(72,73)(74,75)(77,78)(79,80);(71,72,74,75,73)

Polycyclic presentation:

2^2,3,5^2,67|d^a=d^4,e^a=e^4,f^a=f^66,c^b=c^2,d^b=d^4,e^b=e^4

Conjugacy classes & character table

1329 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20100, 142);

D201⋊(C5⋊D5) #34117286