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Dic5×C4⋊C16 #12014607

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productDic5×C4⋊C16

Splittings

SylowC5 ⋊ C4×C4⋊C16

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D5
commutatorC2×C5C2×C4×C16
FittingC2×C5×C4⋊C16C2
socle, prime radicalC23×C5C22×C8
cosocleC22×C5×C8C23
hypercenterC2×C4⋊C16D5
hypocenterC5C4×C4⋊C16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C8 ◁ C2×C4⋊C16

438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 84875);