Finite Group Databasebeta

C4×#11718649 #15784108

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C42

Aliases

direct productC4×#11718649

Splittings

FittingC2×C4×C13×C4⋊C4 ⋊ C2
SylowC13 ⋊ C4×#390

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C22×C42
FrattiniC24C23×D13
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×C4×C4⋊C4D13
hypocenterC13C4×#390
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 90757);