Finite Group Databasebeta

C2×#14531136 #17192528

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#14531136

Splittings

FittingC2×C4×C22⋊C4×C17 ⋊ C2
SylowC17 ⋊ C2×#2273

Subgroups

subgroupG/H
centerC24C23×D17
commutatorC2×C17C23×C42
FrattiniC23C24×D17
FittingC2×C4×C22⋊C4×C17C2
socleC24×C17C24
prime radicalC25×D17C22
cosocleC23×C17C25
hypercenterC2×C4×C22⋊C4D17
hypocenterC17C2×#2273
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

5790 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, 327772);