Finite Group Databasebeta

C2×#14543852 #17960530

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#14543852

Splittings

FittingC22×C16×C17 ⋊ C4
SylowC17 ⋊ C2×#1384

Subgroups

subgroupG/H
centerC2×C4#10587533
commutatorC8×C17C2×C42
FrattiniC2×C8C22×#595
FittingC22×C16×C17C4
socleC22×C17#340
prime radicalC23×D17D8
cosocleC2×C8×D17C23
hypercenterC22×C16#595
hypocenterC17C2×#1384
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

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, 1095774);