Finite Group Databasebeta

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C22×#15689022 #26374626

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#15689022

Splittings

SylowC47 ⋊ C22×#389

Subgroups

subgroupG/H
centerC25C22×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC23×C4⋊C4×C47C2
socle, prime radicalC25×C47C23
cosocleC23×C47C25
hypercenterC23×C4⋊C4D47
hypocenterC47C22×#389
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C25 ◁ C23×C4⋊C4

4894 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 327916);