Finite Group Databasebeta

C2×#20245016 #26368980

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#20245016

Splittings

SylowC47 ⋊ C2×#2117

Subgroups

subgroupG/H
centerC2×C8C2×C22⋊D47
commutatorC4×C47C23×C8
FrattiniC2×C8C23×D47
FittingC22×#131×C47C2
socleC22×C47C2×C22⋊C8
prime radicalC22×#41×C47C4
cosocleC2×C8×C47C24
hypercenterC22×#131D47
hypocenterC47C2×#2117
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ C22×#131

1154 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 322270);