Finite Group Databasebeta

C22×C4×Dic52 #16726936

order3328
isoclinismisoclinic class of #6095
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×C4×Dic52

Splittings

SylowC13 ⋊ C22×C4×Q16

Subgroups

subgroupG/H
centerC23×C4D52
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C4×C8×C13C2
socle, prime radicalC24×C13C2×D4
cosocleC2×C4×C13C25
hypercenterC22×C4×C8D13
hypocenterC13C22×C4×Q16
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×C8

2830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033585);