Finite Group Databasebeta

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C4×#15688957 #26136455

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#15688957

Splittings

SylowC47 ⋊ C4×M64

Subgroups

subgroupG/H
centerC4×C16C2×D47
commutatorC2×C47C2×C4×C16
FrattiniC2×C16C22×D47
FittingC2×C4×C16×C47C2
socleC22×C47C22×C16
prime radicalC23×C47C2×C16
cosocleC2×C16×C47C23
hypercenterC2×C4×C16D47
hypocenterC47C4×M64
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

250 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 89745);