Finite Group Databasebeta

C2×#20241304 #26125252

order12032
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×#20241304

Splittings

SylowC47 ⋊ C2×#1311

Subgroups

subgroupG/H
centerC2×C4×C8C2×D47
commutatorC2×C47C2×C82
FrattiniC4×C8C22×D47
FittingC2×C4×C16×C47C2
socle, prime radicalC23×C47C4×C8
cosocleC4×C8×C47C23
hypercenterC2×C4×C16D47
hypocenterC47C2×#1311
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4×C8 ◁ C2×C4×C16

366 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, 78542);