Finite Group Databasebeta

C2×#20241227 #26105801

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20241227

Splittings

SylowC47 ⋊ C2×#1279

Subgroups

subgroupG/H
centerC23×C4C22⋊D47
commutatorC4×C47C2×C4×C8
FrattiniC2×C42C22×D47
FittingC22×C4⋊C8×C47C2
socle, prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC22×C4⋊C8D47
hypocenterC47C2×#1279
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4⋊C8

974 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 59091);