Finite Group Databasebeta

← Prev (#26232862) Next (#26232864) →

Q8×#13093944 #26232863

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

Aliases

direct productQ8×#13093944

Splittings

FittingQ8×C4⋊C4×C47 ⋊ C2
SylowC47 ⋊ Q8×#102

Subgroups

subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingQ8×C4⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC22×D188C23
cosocleC22×C4×C47C24
hypercenterQ8×C4⋊C4D47
hypocenterC47Q8×#102
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ Q8×C4⋊C4

1314 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 186153);