Finite Group Databasebeta

C2×#14540801 #17910862

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14540801

Splittings

FittingC22×C17×#102 ⋊ C2
SylowC17 ⋊ C2×#3310

Subgroups

subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×#102C2
socleC23×C17C22×D4
prime radicalC2×D4×C22⋊D17C2
hypercenterC22×#102D17
hypocenterC17C2×#3310
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

2578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1046106);