Finite Group Databasebeta

C23×#66869 #15617362

order2816
isoclinismisoclinic class of #4314
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#66869

Splittings

FittingC23×C42×C11 ⋊ C2
SylowC11 ⋊ C23×#104

Subgroups

subgroupG/H
centerC23×C4D44
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC23×C42×C11C2
socleC24×C11C22⋊C4
prime radicalC23×#4339C2
cosocleC2×C4×C11C25
hypercenterC23×C42D11
hypocenterC11C23×#104
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C23×C42

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1033157);