Finite Group Databasebeta

C2×#14539567 #17904878

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

Aliases

direct productC2×#14539567

Splittings

FittingC22×C17×C22⋊C8 ⋊ C2
SylowC17 ⋊ C2×#3190

Subgroups

subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC22×C17×C22⋊C8C2
socleC23×C17C22×D4
prime radicalC2×#11763320C2
hypercenterC22×C22⋊C8D17
hypocenterC17C2×#3190
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

2374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1040122);