Finite Group Databasebeta

Q8×C4⋊(C47⋊C8) #26235072

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

Aliases

direct productQ8×C4⋊(C47⋊C8)

Splittings

SylowC47 ⋊ Q8×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D47
commutatorC22×C47C23×C8
FittingC42×Q8×C47C2
socle, prime radicalC23×C47C23×C4
cosocleC22×C4×C47C24
hypercenterC42×Q8D47
hypocenterC47Q8×C4⋊C8
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C42×Q8

896 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, 188362);