Finite Group Databasebeta

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C2×#20246057 #26375006

order12032
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#20246057

Splittings

FittingC23×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ C2×#2322

Subgroups

subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC23×C4⋊C4×C47C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC23×C4⋊C4D47
hypocenterC47C2×#2322
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4⋊C4

3718 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328296);