Finite Group Databasebeta

C2×#13130385 #16794908

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#13130385

Splittings

SylowC13 ⋊ C2×#1564

Subgroups

subgroupG/H
centerC22×C4C4⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC23×C8×C13C4
socleC23×C13C2×C4⋊C4
prime radicalC24×C13C4⋊C4
cosocleC4×Dic13C24
hypercenterC23×C8#261
hypocenterC13C2×#1564
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1101557);