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#108×#170 #13017367

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct product#108×#170

Splittings

SylowC5 ⋊ C8×#108

Subgroups

subgroupG/H
centerC2×C4D4×AGL(1,𝔽5)
commutatorC4×C5C2×C4×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×#108C4
socleC22×C5C4×C4⋊C4
prime radicalC23×C5C4×Q8
cosocleC2×C4×Dic5C23
hypercenterC2×#108AGL(1,𝔽5)
hypocenterC5C8×#108
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#108

374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1087635);