Finite Group Databasebeta

C2×#14531682 #17193607

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#14531682

Splittings

FittingC2×C17×#385 ⋊ C2
SylowC17 ⋊ C2×D4×C4⋊C4

Subgroups

subgroupG/H
centerC24C23×D17
commutatorC22×C17C24×C4
FrattiniC23C24×D17
FittingC2×C17×#385C2
socleC24×C17C24
prime radicalC23×C22⋊D17C22
cosocleC23×C17C25
hypercenterC2×#385D17
hypocenterC17C2×D4×C4⋊C4
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#385

4718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 328851);