Finite Group Databasebeta

Q8×#10587495 #17050896

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productQ8×#10587495

Splittings

SylowC17 ⋊ Q8×#101

Subgroups

subgroupG/H
centerC22C22×#63227
commutator, prime radicalC23×C17C23×C4
FrattiniC22×C4C23×D17
FittingQ8×M16×C17C2
socleC22×C17C22×C22⋊C4
cosocleC22×C4×C17C24
hypercenterQ8×M16D17
hypocenterC17Q8×#101
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 186140);