Finite Group Databasebeta

C2×#14537820 #17899060

order4352
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#14537820

Splittings

FittingC2×C17×#407 ⋊ C2
SylowC17 ⋊ C2×#2974

Subgroups

subgroupG/H
centerC22×C4C23×D17
commutatorC22×C17C24×C4
FrattiniC2×C4C24×D17
FittingC2×C17×#407C2
socleC23×C17C23×C4
prime radicalC23×C22⋊D17C4
cosocleC2×C4×C17C25
hypercenterC2×#407D17
hypocenterC17C2×#2974
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×#407

2654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1034304);