Finite Group Databasebeta

C2×#14543607 #17950313

order4352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C42

Aliases

direct productC2×#14543607

Splittings

FittingC2×C4×C8×C17 ⋊ C4
SylowC17 ⋊ C2×#1274

Subgroups

subgroupG/H
centerC22×C4C4×#595
commutatorC4×C17C2×C4×C8
FrattiniC42C22×#595
FittingC2×C4×C8×C17C4
socleC23×C17#95
prime radicalC23×D17C22⋊C4
cosocleC42×D17C23
hypercenterC2×C4×C8#595
hypocenterC17C2×#1274
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4×C8

758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1085557);