Finite Group Databasebeta

C2×#14543841 #17960500

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#14543841

Splittings

FittingC2×C17×#107 ⋊ C4
SylowC17 ⋊ C2×#1380

Subgroups

subgroupG/H
centerC23#10587547
commutatorC8×C17C2×C42
FrattiniC2×C8C22×#595
FittingC2×C17×#107C4
socleC23×C17#102
prime radicalC23×D17D8
cosocleC2×C8×D17C23
hypercenterC2×#107#595
hypocenterC17C2×#1380
LCSG ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095744);