Finite Group Databasebeta

C22×C4⋊#6092 #16806988

order3328
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊#6092

Splittings

SylowC13 ⋊ C22×C4⋊C16

Subgroups

subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C23×C16
FrattiniC2×C4C23×#261
FittingC22×C42×C13C4
socle, prime radicalC24×C13C2×C8
cosocleC2×#1055C24
hypercenterC22×C42#261
hypocenterC13C22×C4⋊C16
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C42

862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1113637);