Finite Group Databasebeta

C23×#66879 #15617155

order2816
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210

Aliases

direct productC23×#66879

Splittings

SylowC11 ⋊ C23×#97

Subgroups

subgroupG/H
centerC24×C4C2×D11
commutatorC2×C11C23×C42
FrattiniC2×C4C24×D11
FittingC24×C8×C11C2
socle, prime radicalC25×C11C2×C4
cosocleC2×C4×C11C25
hypercenterC24×C8D11
hypocenterC11C23×#97
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C24×C4 ◁ C24×C8

4126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

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, 1032950);