Finite Group Databasebeta

D17×#1827 #17034164

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

Aliases

direct productD17×#1827

Splittings

FittingC17×#1827 ⋊ C2
SylowC17 ⋊ C2×#1827

Subgroups

subgroupG/H
centerC4#117×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#1827C2
socleC2×C17C2×#381
prime radicalC2×#41×D17C22
cosocleC22×C4×C17C24
hypercenter#1827D17
hypocenterC17C2×#1827
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ #117 ◁ #1827

1354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 169408);