Finite Group Databasebeta

C2×#14526720 #16943443

order4352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#14526720

Splittings

SylowC17 ⋊ C2×#1320

Subgroups

subgroupG/H
centerC2×C4#10587505
commutatorC23×C17C22×C8
FrattiniC2×M16C22×D17
FittingC2×C17×#407C2
socleC22×C17#323
prime radicalC25×C17C8
cosocleC2×M16×C17C23
hypercenterC2×#407D17
hypocenterC17C2×#1320
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#407

626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 78687);