Finite Group Databasebeta

C4×#11718723 #15868813

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

Aliases

direct productC4×#11718723

Splittings

FittingC4×C13×#124 ⋊ C2
SylowC13 ⋊ C4×#454

Subgroups

subgroupG/H
centerC2×C4#88191
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC4×C13×#124C2
socleC22×C13C2×#120
prime radicalC2×#11718723C2
cosocleC22×C4×C13C24
hypercenterC4×#124D13
hypocenterC13C4×#454
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#124

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 175462);