Finite Group Databasebeta

C4×D4×D52 #16022710

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC4×D4×D52

Splittings

FittingC42×D4×C13 ⋊ C2
SylowC13 ⋊ C4×D42

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC42×D4×C13C2
socle, cosocleC23×C13C25
prime radicalC2×D4×D52C2
hypercenterC42×D4D13
hypocenterC13C4×D42
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C42×D4

4804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 329359);