Finite Group Databasebeta

C2×#14528877 #17034103

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14528877

Splittings

FittingC2×C17×#340 ⋊ C2
SylowC17 ⋊ C2×#1825

Subgroups

subgroupG/H
centerC24D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC2×C17×#340C2
socleC24×C17C2×D4
prime radicalC24×D17D4
cosocleC22×C4×C17C24
hypercenterC2×#340D17
hypocenterC17C2×#1825
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

1574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 169347);