Finite Group Databasebeta

C2×#14543958 #17962921

order4352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C210

Aliases

direct productC2×#14543958

Splittings

FittingC24×C4×C17 ⋊ C4
SylowC17 ⋊ C2×C22⋊#95

Subgroups

subgroupG/H
centerC24C22×#595
commutatorC22×C17C22×C42
FrattiniC23C23×#595
FittingC24×C4×C17C4
socleC24×C17C22×C4
prime radicalC25×D17C22
cosocleC23×D17C24
hypercenterC24×C4#595
hypocenterC17C2×C22⋊#95
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C24 ◁ C24×C4

7630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1098165);