Finite Group Databasebeta

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#13031330

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

No aliases for this group.

Splittings

SylowC5 ⋊ #17795

Subgroups

subgroupG/H
centerC2×C4C2×C4⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC22×C5×M16C4
socleC22×C5C22×C4⋊C4
prime radicalC24×C5C4⋊C4
cosocleC4×Dic5C24
hypercenterC22×M16AGL(1,𝔽5)
hypocenterC5#17795
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Polycyclic presentation:

2^8,5|a^2=f,b^2=e,d^2=g,e^2=g,f^2=h,b^a=be,c^a=ch,e^a=eg,i^a=i^2,c^b=cg,i^f=i^4

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1101598);