Finite Group Databasebeta

C22×#11718851 #16732350

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#11718851

Splittings

FittingC23×C13×Q16 ⋊ C2
SylowC13 ⋊ C22×#497

Subgroups

subgroupG/H
centerC24D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC23×C13×Q16C2
socleC24×C13C2×D4
prime radicalC23×D52C22
hypercenterC23×Q16D13
hypocenterC13C22×#497
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×Q16

3350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1038999);