Finite Group Databasebeta

Q8×(C2×D47)⋊C8 #26232791

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

Aliases

direct productQ8×(C2×D47)⋊C8

Splittings

FittingC2×C8×Q8×C47 ⋊ C2
SylowC47 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC2×C8×Q8×C47C2
socleC23×C47C23×C4
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenterC2×C8×Q8D47
hypocenterC47Q8×C22⋊C8
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

1356 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 186081);