Finite Group Databasebeta

C2×#14544827 #17970090

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

Aliases

direct productC2×#14544827

Splittings

FittingC2×C17×#127 ⋊ C4
SylowC17 ⋊ C2×#1910

Subgroups

subgroupG/H
centerC22#11763757
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×#127C4
socleC22×C17#386
prime radicalC2×#11763372C2
cosocleC2×C4×D17C24
hypercenterC2×#127#595
hypocenterC17C2×#1910
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

1878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1105334);