Finite Group Databasebeta

C2×#14537718 #17898689

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14537718

Splittings

SylowC17 ⋊ C2×#2960

Subgroups

subgroupG/H
centerC22×C8C22×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC22×C4×C8×C17C2
socleC23×C17C23×C4
prime radicalC24×C17C22×C4
cosocleC2×C4×C17C25
hypercenterC22×C4×C8D17
hypocenterC17C2×#2960
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

1982 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1033933);