Finite Group Databasebeta

D4×#10587506 #17049756

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

Aliases

direct productD4×#10587506

Splittings

SylowC17 ⋊ D4×#103

Subgroups

subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×D4×Q8×C17C2
socleC23×C17C22×D4
prime radicalC22×D4×C17D4
cosocleC22×C4×C17C24
hypercenterC2×D4×Q8D17
hypocenterC17D4×#103
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

1530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 185000);