Finite Group Databasebeta

C4×#11719623 #16807459

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#11719623

Splittings

FittingC2×C4×D4×C13 ⋊ C4
SylowC13 ⋊ C4×#518

Subgroups

subgroupG/H
centerC2×C4C23×#261
commutatorC2×C13C23×C42
FrattiniC22C24×#261
FittingC2×C4×D4×C13C4
socleC22×C13C24×C4
prime radicalC22×D4×D13C22
cosocleC22×D13C25
hypercenterC2×C4×D4#261
hypocenterC13C4×#518
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×D4

4186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114108);