Finite Group Databasebeta

C2×#14542941 #17941447

order4352
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#14542941

Splittings

FittingC2×C17×H(3,𝔽4) ⋊ C2
SylowC17 ⋊ C2×#3532

Subgroups

subgroupG/H
centerC23C24×D17
commutator, cosocleC22×C17C26
FrattiniC22C25×D17
FittingC2×C17×H(3,𝔽4)C2
socleC23×C17C25
hypercenterC2×H(3,𝔽4)D17
hypocenterC17C2×#3532
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×H(3,𝔽4)

9542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1076691);