Finite Group Databasebeta

C4×#11719371 #16025605

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#11719371

Splittings

FittingC4×C13×#123 ⋊ C2
SylowC13 ⋊ C4×#560

Subgroups

subgroupG/H
centerC22×C4C23×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC4×C13×#123C2
socle, cosocleC23×C13C25
prime radicalC2×#11719371C2
hypercenterC4×#123D13
hypocenterC13C4×#560
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×#123

2568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 332254);