Finite Group Databasebeta

Q8×#10587538 #17978670

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24

Aliases

direct productQ8×#10587538

Splittings

SylowC17 ⋊ Q8×M32

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×#595
commutator, socleC22×C17C23×C8
FittingC2×C4×Q8×C17C4
prime radicalC23×C17C22×C8
cosocleC2×#3622C24
hypercenterC2×C4×Q8#595
hypocenterC17Q8×M32
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8

530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113914);