Finite Group Databasebeta

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C4×#15689767 #26376074

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

Aliases

direct productC4×#15689767

Splittings

FittingC22×C4×D4×C47 ⋊ C2
SylowC47 ⋊ C4×#546

Subgroups

subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC22×C4×D4×C47C2
socle, cosocleC23×C47C25
prime radicalC2×#15689767C2
hypercenterC22×C4×D4D47
hypocenterC47C4×#546
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

3720 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, 329364);