Finite Group Databasebeta

C22×#11718502 #16729702

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11718502

Splittings

FittingC22×C13×C4⋊C8 ⋊ C2
SylowC13 ⋊ C22×#461

Subgroups

subgroupG/H
centerC24C2×D52
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×C4⋊C8C2
socleC24×C13C2×D4
prime radicalC23×D52C22
hypercenterC22×C4⋊C8D13
hypocenterC13C22×#461
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4⋊C8

3222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036351);