Finite Group Databasebeta

D17×#1376 #16949175

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C24

Aliases

direct productD17×#1376

Splittings

FittingC17×#1376 ⋊ C2
SylowC17 ⋊ C2×#1376

Subgroups

subgroupG/H
centerC2×C8D4×D17
commutatorC4×C17C2×C4×C8
FrattiniC22×C8C22×D17
FittingC17×#1376C2
socleC22×C17C2×C4⋊C8
prime radicalC23×D17M16
cosocleC22×C8×C17C23
hypercenter#1376D17
hypocenterC17C2×#1376
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1376

670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84419);