Finite Group Databasebeta

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C22⋊C4×#10625350 #26375480

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

Aliases

direct productC22⋊C4×#10625350

Splittings

FittingC2×C4×C22⋊C4×C47 ⋊ C2
SylowC47 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC23×#10625350C2
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C22⋊C4×#41
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

5646 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328770);