Finite Group Databasebeta

C22×#11718372 #16726965

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11718372

Splittings

FittingC22×C13×#97 ⋊ C2
SylowC13 ⋊ C22×#442

Subgroups

subgroupG/H
centerC24C2×D52
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#97C2
socleC24×C13C2×D4
prime radicalC23×D104C2
cosocleC2×C4×C13C25
hypercenterC22×#97D13
hypocenterC13C22×#442
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

3654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033614);