Finite Group Databasebeta

C2×#20244984 #26368912

order12032
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#20244984

Splittings

SylowC47 ⋊ C2×#2108

Subgroups

subgroupG/H
centerC22×C16C2×D47
commutatorC2×C47C22×C4×C8
FrattiniC2×C8C23×D47
FittingC23×C16×C47C2
socleC23×C47C22×C8
prime radicalC24×C47C2×C8
cosocleC2×C8×C47C24
hypercenterC23×C16D47
hypocenterC47C2×#2108
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C16 ◁ C23×C16

854 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322202);