Finite Group Databasebeta

C22×#11718756 #16729538

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11718756

Splittings

FittingC22×C13×C4⋊Q8 ⋊ C2
SylowC13 ⋊ C22×#456

Subgroups

subgroupG/H
centerC23#88191
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×C4⋊Q8C2
socleC23×C13#120
prime radicalC22×#88254C2
hypercenterC22×C4⋊Q8D13
hypocenterC13C22×#456
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊Q8

4766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1036187);