Finite Group Databasebeta

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C4×#19104763 #35223348

order20864
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#19104763

Splittings

FittingC4×M16×C163 ⋊ C2
SylowC163 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×D652
commutatorC4×C163C23×C4
FrattiniC2×C4C23×D163
FittingC4×M16×C163C2
socleC22×C163C22×D4
prime radicalC2×#19104763C2
cosocleC2×C4×C163C24
hypercenterC4×M16D163
hypocenterC163C4×AGL(1,ℤ/8)
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5216

Conjugacy classes & character table

3284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 13322);