Finite Group Databasebeta

C22×#11718680 #16729701

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

Aliases

direct productC22×#11718680

Splittings

SylowC13 ⋊ C22×#461

Subgroups

subgroupG/H
centerC24C2×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C4×D4×C13C2
socleC24×C13C2×D4
prime radicalC23×D4×C13C22
hypercenterC22×C4×D4D13
hypocenterC13C22×#461
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×D4

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, 1036350);