Finite Group Databasebeta

C22×#11718267 #16796763

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC22×#11718267

Splittings

FittingC23×C8×C13 ⋊ C4
SylowC13 ⋊ C22×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC22×C4C4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC23×C8×C13C4
socleC23×C13#95
prime radicalC24×D13D4
cosocleC2×C4×D13C24
hypercenterC23×C8#261
hypocenterC13C22×H(3,ℤ/4)
LCSG ▷ C4×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C8

2270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103412);