Finite Group Databasebeta

C2×#14546004 #17983174

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14546004

Splittings

SylowC17 ⋊ C2×#2171

Subgroups

subgroupG/H
centerC22D4×#3633
commutatorC4×C17C23×C8
FrattiniC4C23×#3633
FittingC2×SD16×C17C8
socleC22×C17C8×D4
prime radicalC2×#10587602C4
cosocle#63242C24
hypercenterC2×SD16#3633
hypocenterC17C2×#2171
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1118418);