Finite Group Databasebeta

Q8×#16862558 #46800711

order33952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productQ8×#16862558

Splittings

FittingQ8×C1061 ⋊ C4
SylowC1061 ⋊ C4×Q8

Subgroups

subgroupG/H
center, FrattiniC2C22×#16862558
commutator, socleC2×C1061C22×C4
FittingQ8×C1061C4
prime radical, cosocleC2×D1061C23
hypercenterQ8#16862558
hypocenterC1061C4×Q8
LCSG ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C2 ◁ Q8

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8488

Conjugacy classes & character table

1345 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 227);