Finite Group Databasebeta

D17×#1374 #16949159

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C25

Aliases

direct productD17×#1374

Splittings

FittingC17×#1374 ⋊ C2
SylowC17 ⋊ C2×#1374

Subgroups

subgroupG/H
center, FrattiniC22×C8C22×D17
commutatorC2×C17C2×C4×C16
FittingC17×#1374C2
socleC23×C17C22×C8
prime radicalC23×D17C2×C8
cosocleC22×C8×C17C23
hypercenter#1374D17
hypocenterC17C2×#1374
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ #1374

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84403);