Finite Group Databasebeta

C2×#14526862 #16949161

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14526862

Splittings

SylowC17 ⋊ C2×#1374

Subgroups

subgroupG/H
centerC23×C8C2×D17
commutatorC2×C17C2×C4×C16
FrattiniC22×C8C22×D17
FittingC22×C4×C8×C17C2
socle, prime radicalC24×C17C2×C8
cosocleC22×C8×C17C23
hypercenterC22×C4×C8D17
hypocenterC17C2×#1374
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4352

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 84405);