Finite Group Databasebeta

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C4×#15689032 #26138064

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#15689032

Splittings

FittingC2×C4×C22⋊C4×C47 ⋊ C2
SylowC47 ⋊ C4×#392

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC2×#15689032C2
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C4×#392
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

3502 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, 91354);