Finite Group Databasebeta

C2×#20245290 #26369758

order12032
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20245290

Splittings

SylowC47 ⋊ C2×Q8×C16

Subgroups

subgroupG/H
centerC22×C8C22×D47
commutatorC2×C47C23×C16
FrattiniC2×C8C23×D47
FittingC2×C47×C4⋊C16C2
socle, prime radicalC23×C47C22×C8
cosocleC2×C8×C47C24
hypercenterC2×C4⋊C16D47
hypocenterC47C2×Q8×C16
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C2×C4⋊C16

582 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 323048);