Finite Group Databasebeta

D4×#10587507 #17049694

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#10587507

Splittings

SylowC17 ⋊ D4×#101

Subgroups

subgroupG/H
centerC22C22×C22⋊Dic17
commutatorC23×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×D4×Q8×C17C2
socleC22×C17C22×C22⋊C4
prime radicalC22×D4×C17C2×C4
cosocleC22×C4×C17C24
hypercenterC2×D4×Q8D17
hypocenterC17D4×#101
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×D4×Q8

1378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 184938);