Finite Group Databasebeta

C2×#14530519 #17187265

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

Aliases

direct productC2×#14530519

Splittings

FittingC2×C17×#427 ⋊ C2
SylowC17 ⋊ C2×#2145

Subgroups

subgroupG/H
centerC2×C4#10587480
commutatorC8×C17C23×C4
FrattiniC2×C8C23×D17
FittingC2×C17×#427C2
socleC22×C17C2×#102
prime radicalC22×#10587590C2
cosocleC2×C8×C17C24
hypercenterC2×#427D17
hypocenterC17C2×#2145
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

1170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322509);