Finite Group Databasebeta

C2×#20241465 #26131114

order12032
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20241465

Splittings

SylowC47 ⋊ C2×#1374

Subgroups

subgroupG/H
centerC23×C8C2×D47
commutatorC2×C47C2×C4×C16
FrattiniC22×C8C22×D47
FittingC23×C16×C47C2
socle, prime radicalC24×C47C2×C8
cosocleC22×C8×C47C23
hypercenterC23×C16D47
hypocenterC47C2×#1374
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C23×C8 ◁ C23×C16

726 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, 84404);