Finite Group Databasebeta

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C4×#15688849 #26106784

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#15688849

Splittings

SylowC47 ⋊ C4×#324

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic47
commutatorC22×C47C2×C4×C8
FrattiniC23×C4C22×D47
FittingC2×C4×C4⋊C4×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22×C4
cosocleC23×C4×C47C23
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C4×#324
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

730 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 60074);