Finite Group Databasebeta

C2×#14537808 #17899046

order4352
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×#14537808

Splittings

SylowC17 ⋊ C2×#2972

Subgroups

subgroupG/H
centerC22×C4C23×D17
commutatorC2×C17C24×C8
FrattiniC2×C4C24×D17
FittingC22×C4×D4×C17C2
socleC23×C17C23×C4
prime radicalC23×D4×C17C4
cosocleC2×C4×C17C25
hypercenterC22×C4×D4D17
hypocenterC17C2×#2972
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C4×D4

2890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1034290);