Finite Group Databasebeta

C2×#20241401 #26126502

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

Aliases

direct productC2×#20241401

Splittings

SylowC47 ⋊ C2×#1348

Subgroups

subgroupG/H
centerC23#13093946
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×C22⋊C16C2
socleC23×C47#102
prime radicalC24×C47D8
cosocleC22×C8×C47C23
hypercenterC2×C22⋊C16D47
hypocenterC47C2×#1348
LCSG ▷ C2×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

506 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1898 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 79792);