Finite Group Databasebeta

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C4×#15689319 #26222456

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#15689319

Splittings

FittingC4×C4⋊C8×C47 ⋊ C2
SylowC47 ⋊ C4×#459

Subgroups

subgroupG/H
centerC22×C4C2×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×C4⋊C8×C47C2
socleC23×C47C22×D4
prime radicalC2×#15689319C2
cosocleC22×C4×C47C24
hypercenterC4×C4⋊C8D47
hypocenterC47C4×#459
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

1272 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 175746);