Finite Group Databasebeta

C2×#14528819 #17033935

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

Aliases

direct productC2×#14528819

Splittings

FittingC22×C17×#108 ⋊ C2
SylowC17 ⋊ C2×#1810

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC22×C17×#108C2
socleC23×C17C2×C4⋊C4
prime radicalC24×D17Q8
cosocleC22×C4×C17C24
hypercenterC22×#108D17
hypocenterC17C2×#1810
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#108

1566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 169179);