Finite Group Databasebeta

C2×#14544871 #17970253

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14544871

Splittings

FittingC2×C17×#101 ⋊ C4
SylowC17 ⋊ C2×#1932

Subgroups

subgroupG/H
centerC22#11763759
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×#101C4
socleC22×C17#388
prime radicalC22×#63256C22
cosocleC2×C4×D17C24
hypercenterC2×#101#595
hypocenterC17C2×#1932
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

1046 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1105497);