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M16×5−1+2 #14522261

order2000
nilpotency class2
isoclinismisoclinic class of D4×H(3,𝔽5)
automorphism?
homologyAbelianization (H1) = C2×C4×C52 · Schur multiplier (H2) = C1

Aliases

direct productM16×5−1+2
unambiguous semidirect product(M16×C25)⋊C5

Subgroups

subgroupG/H
center, Frattini, cosocleC4×C5C22×C52
commutator, socleC2×C5C2×C4×C52
prime radicalC22×C52C4×C5
LCSG ▷ C2×C5 ▷ C1
UCSC1 ◁ C4×C5 ◁ G

100 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);(2,6)(4,8)(10,13,20,21,14)(12,17,18,19,27)(16,24,28,25,26)(23,30,31,32,33)

Conjugacy classes & character table

290 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofM16×D25⋊C5, M16×AGL(1,ℤ/25), #72275752, …
maximal subgroup ofM16×D25⋊C5, AGL(1,ℤ/8)×5−1+2, #72275752, …
maximal normal subgroup ofM16×D25⋊C5, AGL(1,ℤ/8)×5−1+2, #72275752, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 224);