Finite Group Databasebeta

C2×#14543869 #17960567

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14543869

Splittings

FittingC22×C22⋊C4×C17 ⋊ C4
SylowC17 ⋊ C2×#1390

Subgroups

subgroupG/H
centerC23#10587539
commutatorC23×C17C2×C42
FrattiniC24C22×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17#99
prime radicalC23×C22⋊D17C22
cosocleC22×C22⋊D17C23
hypercenterC22×C22⋊C4#595
hypocenterC17C2×#1390
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24 ◁ C25 ◁ C22×C22⋊C4

1202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095811);