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Q8×#4130 #13043967

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productQ8×#4130

Splittings

FittingC2×C4×C5×Q8 ⋊ C4
SylowC5 ⋊ Q8×#117

Subgroups

subgroupG/H
centerC2×C4C23×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
prime radicalC23×D5C24
cosocleC22×D5C25
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5Q8×#117
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

2434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 1114235);