Finite Group Databasebeta

C4×#11718855 #16016199

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#11718855

Splittings

FittingC4×C13×#135 ⋊ C2
SylowC13 ⋊ C4×#508

Subgroups

subgroupG/H
centerC42#6104
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC4×C13×#135C2
socleC22×C13C22×D8
prime radicalC2×#11718855C2
cosocleC2×C8×C13C24
hypercenterC4×#135D13
hypocenterC13C4×#508
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322848);