Finite Group Databasebeta

D4×#10587587 #17898285

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productD4×#10587587

Splittings

FittingC2×C8×D4×C17 ⋊ C2
SylowC17 ⋊ D4×#131

Subgroups

subgroupG/H
centerC2×C8C23×D17
commutator, socleC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C8×D4×C17C2
prime radicalD4×#63252C2
cosocleC2×C4×C17C25
hypercenterC2×C8×D4D17
hypocenterC17D4×#131
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C2×C8×D4

2814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033529);