Finite Group Databasebeta

C23×#66925 #15660331

order2816
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4

Aliases

direct productC23×#66925

Splittings

FittingC23×C42×C11 ⋊ C2
SylowC11 ⋊ C23×#117

Subgroups

subgroupG/H
centerC24×C4C2×D11
commutatorC2×C11C25×C4
FrattiniC22C25×D11
FittingC23×C42×C11C2
socleC25×C11C23
prime radicalC25×D11C22
cosocleC22×C11C26
hypercenterC23×C42D11
hypocenterC11C23×#117
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C24×C4 ◁ C23×C42

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076126);