Finite Group Databasebeta

C2×#14530622 #17187553

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14530622

Splittings

FittingC2×C4×C16×C17 ⋊ C2
SylowC17 ⋊ C2×#2170

Subgroups

subgroupG/H
centerC2×C16D68
commutatorC4×C17C23×C8
FrattiniC2×C8C23×D17
FittingC2×C4×C16×C17C2
socleC22×C17C8×D4
prime radicalC2×#10587590C4
cosocleC2×C8×C17C24
hypercenterC2×C4×C16D17
hypocenterC17C2×#2170
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C16 ◁ C22×C16 ◁ C2×C4×C16

662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 322797);