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D8×5−1+2 #14522264

order2000
nilpotency class3
isoclinismisoclinic class of D8×H(3,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2

Aliases

direct productD8×5−1+2
unambiguous semidirect product(D8×C25)⋊C5

Subgroups

subgroupG/H
center, socleC2×C5C52×D4
commutator, Frattini, cosocleC4×C5C22×C52
prime radicalC52×D8C5
LCSG ▷ C4×C5 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C4×5−1+2 ◁ G

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 200

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4,5,6,7,8)(9,10,12,16,23,11,14,18,25,30,15,21,27,24,31,22,20,17,26,32,29,13,19,28,33);(2,8)(3,7)(4,6)(10,13,20,21,14)(12,17,18,19,27)(16,24,28,25,26)(23,30,31,32,33)

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD8×D25⋊C5, #72275753, D8×AGL(1,ℤ/25), …
maximal subgroup ofD8×D25⋊C5, AGL(1,ℤ/8)×5−1+2, #72275753
maximal normal subgroup ofD8×D25⋊C5, AGL(1,ℤ/8)×5−1+2, #72275753

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 227);