Finite Group Databasebeta

C2×#14541920 #17940830

order4352
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14541920

Splittings

FittingC22×C17×M32 ⋊ C2
SylowC17 ⋊ C2×#3414

Subgroups

subgroupG/H
centerC2×C4C2×D136
commutator, cosocleC8×C17C25
FrattiniC8C24×D17
FittingC22×C17×M32C2
socleC22×C17C22×D8
hypercenterC22×M32D17
hypocenterC17C2×#3414
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

2098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076074);