Finite Group Databasebeta

C2×C8×#10625325 #26185643

order12032
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×C8×#10625325

Splittings

FittingC2×C82×C47 ⋊ C2
SylowC47 ⋊ C2×C8×SD16

Subgroups

subgroupG/H
centerC22×C8D188
commutatorC4×C47C23×C8
FrattiniC42C23×D47
FittingC2×C82×C47C2
socleC23×C47C4×D4
prime radicalC22×D188C2×C4
cosocleC42×C47C24
hypercenterC2×C82D47
hypocenterC47C2×C8×SD16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C2×C82

822 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 138933);