Finite Group Databasebeta

C2×C4×D4×#261 #16807449

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C4×D4×#261
unambiguous semidirect productD13⋊(C42×D4)

Splittings

FittingC2×C4×D4×C13 ⋊ C4
SylowC13 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC2×C13C23×C42
FrattiniC22C24×#261
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×D4×D13C22
cosocleC22×D13C25
hypercenterC2×C4×D4#261
hypocenterC13C2×C42×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114098);