Finite Group Databasebeta

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C22×#15688885 #26213673

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productC22×#15688885

Splittings

SylowC47 ⋊ C22×#340

Subgroups

subgroupG/H
centerC25C22⋊D47
commutatorC4×C47C22×C42
FrattiniC22×C4C23×D47
FittingC23×C4⋊C4×C47C2
socle, prime radicalC25×C47D4
cosocleC22×C4×C47C24
hypercenterC23×C4⋊C4D47
hypocenterC47C22×#340
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

3006 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, 166963);