Finite Group Databasebeta

C2×#14527593 #17003706

order4352
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14527593

Splittings

SylowC17 ⋊ C2×SD16⋊C8

Subgroups

subgroupG/H
centerC22×C4D4×D17
commutatorC4×C17C23×C8
FrattiniC42C23×D17
FittingC2×C17×D4⋊C8C2
socleC23×C17C4×D4
prime radicalC22×D4×C17C2×C4
cosocleC42×C17C24
hypercenterC2×D4⋊C8D17
hypocenterC17C2×SD16⋊C8
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2176

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, 138950);