Finite Group Databasebeta

D17×#1299 #16924482

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productD17×#1299

Splittings

FittingC17×#1299 ⋊ C2
SylowC17 ⋊ C2×#1299

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D17
commutatorC2×C4×C17C2×C42
FrattiniC2×C42C22×D17
FittingC17×#1299C2
socleC22×C17C2×#95
prime radicalC23×D17C4⋊C4
cosocleC2×C42×C17C23
hypercenter#1299D17
hypocenterC17C2×#1299
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1299

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 59726);