Finite Group Databasebeta

C2×#20241350 #26126010

order12032
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20241350

Splittings

FittingC2×C4×C16×C47 ⋊ C2
SylowC47 ⋊ C2×#1331

Subgroups

subgroupG/H
centerC22×C4D376
commutatorC8×C47C22×C8
FrattiniC4×C8C22×D47
FittingC2×C4×C16×C47C2
socleC23×C47#102
prime radicalC22×D376C4
cosocleC4×C8×C47C23
hypercenterC2×C4×C16D47
hypocenterC47C2×#1331
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×C16

470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 79300);