Finite Group Databasebeta

C2×D13⋊#364 #16807008

order3328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×D13⋊#364
unambiguous semidirect productD13⋊(C2×#364)

Splittings

SylowC13 ⋊ C22×#364

Subgroups

subgroupG/H
centerC2×C8C4⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC2×C4×C8×C13C4
socleC22×C13C2×C4⋊C8
prime radicalC23×D13M16
cosocleC2×#1055C24
hypercenterC2×C4×C8#261
hypocenterC13C22×#364
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×C4×C8

782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1113657);