Finite Group Databasebeta

C2×#14544995 #17978131

order4352
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#14544995

Splittings

SylowC17 ⋊ C2×#2108

Subgroups

subgroupG/H
centerC22×C4C22×#595
commutatorC2×C17C22×C4×C8
FrattiniC2×C4C23×#595
FittingC22×M16×C17C4
socleC23×C17C22×C8
prime radicalC24×C17C2×C8
cosocleC2×#3622C24
hypercenterC22×M16#595
hypocenterC17C2×#2108
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×M16

854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1113375);