Finite Group Databasebeta

C22×D13⋊(C4⋊C8) #16808119

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×D13⋊(C4⋊C8)
unambiguous semidirect productD13⋊(C22×C4⋊C8)

Splittings

SylowC13 ⋊ C23×C4⋊C8

Subgroups

subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C24×C8
FrattiniC22C24×#261
FittingC22×C42×C13C4
socleC24×C13C22×C4
prime radicalC24×D13C2×C4
cosocleC2×Dic13C25
hypercenterC22×C42#261
hypocenterC13C23×C4⋊C8
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C42

3870 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114768);