Finite Group Databasebeta

C2×#14530513 #17187253

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#14530513

Splittings

FittingC22×C17×M32 ⋊ C2
SylowC17 ⋊ C2×#2143

Subgroups

subgroupG/H
centerC2×C4C2×D136
commutatorC8×C17C23×C4
FrattiniC2×C8C23×D17
FittingC22×C17×M32C2
socleC22×C17C2×#102
prime radicalC22×#10587590C2
cosocleC2×C8×C17C24
hypercenterC22×M32D17
hypocenterC17C2×#2143
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C22×M32

1154 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, 322497);