Finite Group Databasebeta

C2×#20245274 #26369684

order12032
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#20245274

Splittings

SylowC47 ⋊ C2×#2179

Subgroups

subgroupG/H
centerC2×C4D8×D47
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
Fitting, prime radicalC2×C47×#508C2
socleC22×C47C4×D8
cosocleC2×C8×C47C24
hypercenterC2×#508D47
hypocenterC47C2×#2179
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

654 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322974);