Finite Group Databasebeta

C2×#14529234 #17036102

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14529234

Splittings

FittingC22×C17×#99 ⋊ C2
SylowC17 ⋊ C2×#1898

Subgroups

subgroupG/H
centerC23C22⋊C4×D17
commutatorC23×C17C23×C4
FrattiniC24C23×D17
FittingC22×C17×#99C2
socleC23×C17C2×C22⋊C4
prime radicalC22×#10587623C2
cosocleC24×C17C24
hypercenterC22×#99D17
hypocenterC17C2×#1898
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

3746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 171346);