Finite Group Databasebeta

C2×#14543886 #17960641

order4352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#14543886

Splittings

FittingC2×C17×#101 ⋊ C4
SylowC17 ⋊ C2×#1395

Subgroups

subgroupG/H
centerC22#11763686
commutatorC2×C4×C17C2×C42
FrattiniC2×Q8C22×#595
FittingC2×C17×#101C4
socleC22×C17#342
prime radicalC22×#63256C22
cosocleC2×#63256C23
hypercenterC2×#101#595
hypocenterC17C2×#1395
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1095885);