Finite Group Databasebeta

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C4×#19127962 #35411265

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#19127962

Splittings

SylowC83 ⋊ C4×#471

Subgroups

subgroupG/H
centerC2×C4#14581764
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC4×AGL(1,ℤ/8)×C83C2
socleC22×C83C2×#121
prime radicalC2×AGL(1,ℤ/8)×C83C22
cosocleC22×C4×C83C24
hypercenterC4×AGL(1,ℤ/8)D83
hypocenterC83C4×#471
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

914 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1868 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 176429);