Finite Group Databasebeta

C4×#11718801 #16015564

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11718801

Splittings

SylowC13 ⋊ C4×#504

Subgroups

subgroupG/H
centerC4×C8C22×D13
commutatorC2×C13C22×C4×C8
FrattiniC2×C8C23×D13
FittingC4×C13×#131C2
socleC22×C13C23×C8
prime radicalC2×C13×#41C2×C4
cosocleC2×C8×C13C24
hypercenterC4×#131D13
hypocenterC13C4×#504
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C8 ◁ C4×#131

834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322213);