Finite Group Databasebeta

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C2×#20241291 #26106567

order12032
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241291

Splittings

SylowC47 ⋊ C2×#1303

Subgroups

subgroupG/H
centerC22×C4(C2×D47)⋊C4
commutatorC2×C4×C47C2×C42
FrattiniC2×C42C22×D47
FittingC2×C4×C4⋊C4×C47C2
socleC23×C47#95
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C2×#1303
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

810 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, 59857);