Finite Group Databasebeta

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C2×C4⋊#3926 #12019780

order1280
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊#3926

Splittings

SylowC5 ⋊ C2×C4⋊C32

Subgroups

subgroupG/H
centerC22×C16C2×D5
commutatorC2×C5C22×C32
FrattiniC2×C16C22×D5
FittingC2×C4×C5×C16C2
socle, prime radicalC23×C5C2×C16
cosocleC2×C5×C16C23
hypercenterC2×C4×C16D5
hypocenterC5C2×C4⋊C32
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C16 ◁ C2×C4×C16

230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 90048);