Finite Group Databasebeta

C2×#20241426 #26127484

order12032
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#20241426

Splittings

SylowC47 ⋊ C2×#1358

Subgroups

subgroupG/H
centerC22#15688866
commutatorC42×C47C22×C4
FrattiniC4×C8C22×D47
FittingC2×C47×#364C2
socleC22×C47#331
prime radicalC23×C47#100
cosocleC4×C8×C47C23
hypercenterC2×#364D47
hypocenterC47C2×#1358
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#364

390 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1334 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 80774);