Finite Group Databasebeta

C2×C4×#13094021 #26374792

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

Aliases

direct productC2×C4×#13094021

Splittings

FittingC2×C43×C47 ⋊ C2
SylowC47 ⋊ C2×C4×#127

Subgroups

subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C43×C47C2
socleC24×C47C24
prime radicalC22×#13094021C2
cosocleC23×C47C25
hypercenterC2×C43D47
hypocenterC47C2×C4×#127
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×C43

5694 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 328082);