Finite Group Databasebeta

C4×#11718907 #15868826

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#11718907

Splittings

SylowC13 ⋊ C4×#456

Subgroups

subgroupG/H
centerC2×C4#88207
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×2−1+4C2
socleC22×C13C2×#120
prime radicalC2×C13×2−1+4C22
cosocleC22×C4×C13C24
hypercenterC4×2−1+4D13
hypocenterC13C4×#456
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×2−1+4

1358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 175475);