Finite Group Databasebeta

C2×#20241476 #26131146

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241476

Splittings

SylowC47 ⋊ C2×#1379

Subgroups

subgroupG/H
centerC22×C8D188
commutatorC4×C47C2×C4×C8
FrattiniC22×C8C22×D47
FittingC23×C16×C47C2
socleC23×C47C22⋊C8
prime radicalC24×C47M16
cosocleC22×C8×C47C23
hypercenterC23×C16D47
hypocenterC47C2×#1379
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C23×C16

606 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, 84436);