Finite Group Databasebeta

C2×#20243380 #26215693

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20243380

Splittings

SylowC47 ⋊ C2×#1800

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×C4×D4×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D4×C47C22
cosocleC22×C4×C47C24
hypercenterC22×C4×D4D47
hypocenterC47C2×#1800
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×D4

1842 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 168983);