Finite Group Databasebeta

C2×#14543880 #17960620

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

Aliases

direct productC2×#14543880

Splittings

FittingC2×C17×#101 ⋊ C4
SylowC17 ⋊ C2×#1394

Subgroups

subgroupG/H
centerC22#11763686
commutatorC2×C4×C17C2×C42
FrattiniC2×Q8C22×#595
FittingC2×C17×#101C4
socleC22×C17#342
prime radicalC23×D17C22⋊C4
cosocleC2×Q8×D17C23
hypercenterC2×#101#595
hypocenterC17C2×#1394
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 544

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, 1095864);