Finite Group Databasebeta

C2×#14531943 #17196923

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#14531943

Splittings

FittingC2×C17×#381 ⋊ C2
SylowC17 ⋊ C2×#2377

Subgroups

subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#381C2
socleC24×C17C24
prime radicalC22×#10587616C2
cosocleC23×C17C25
hypercenterC2×#381D17
hypocenterC17C2×#2377
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#381

3302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 332167);