Finite Group Databasebeta

C22×C4⋊C4×#261 #16807446

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4⋊C4×#261

Splittings

FittingC22×C13×C4⋊C4 ⋊ C4
SylowC13 ⋊ C22×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC2×C13C23×C42
FrattiniC22C24×#261
FittingC22×C13×C4⋊C4C4
socleC24×C13C22×C4
prime radicalC24×D13C23
cosocleC22×D13C25
hypercenterC22×C4⋊C4#261
hypocenterC13C22×C4×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4⋊C4

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114095);