Finite Group Databasebeta

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C2×#20243409 #26215816

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20243409

Splittings

FittingC2×C4×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C2×#1806

Subgroups

subgroupG/H
centerC22×C4C2×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C4×C4⋊C4×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC22×#10625350C22
cosocleC22×C4×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C2×#1806
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

1618 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1916 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 169106);