Finite Group Databasebeta

C22×C4×C4⋊Dic13 #16021097

order3328
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4×C4⋊Dic13

Splittings

SylowC13 ⋊ C22×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24×C4C2×D13
commutatorC2×C13C23×C42
FrattiniC23C24×D13
FittingC23×C42×C13C2
socle, prime radicalC25×C13C23
cosocleC23×C13C25
hypercenterC23×C42D13
hypocenterC13C22×C4×C4⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24×C4 ◁ C23×C42

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327746);