Finite Group Databasebeta

C22×#10622852 #15620100

order2816
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC22×#10622852

Splittings

SylowC11 ⋊ C22×#452

Subgroups

subgroupG/H
centerC24C2×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC23×C11×#41C2
socleC24×C11C2×D4
hypercenterC23×#41D11
hypocenterC11C22×#452
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×#41

5110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1035895);