Finite Group Databasebeta

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C22×#15688844 #26181846

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×#15688844

Splittings

SylowC47 ⋊ C22×#322

Subgroups

subgroupG/H
centerC22×C42C2×D47
commutatorC2×C47C22×C4×C8
FrattiniC42C23×D47
FittingC22×C4×C8×C47C2
socle, prime radicalC24×C47C42
cosocleC42×C47C24
hypercenterC22×C4×C8D47
hypocenterC47C22×#322
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

1182 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, 135136);