Finite Group Databasebeta

C22×#11719285 #16769603

order3328
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#11719285

Splittings

FittingC22×C4×Q8×C13 ⋊ C2
SylowC13 ⋊ C22×#529

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC22×C4×Q8×C13C2
socleC24×C13C24
prime radicalC22×#88149C2
hypercenterC22×C4×Q8D13
hypocenterC13C22×#529
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

8670 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, 1076252);