Finite Group Databasebeta

C2×#13081819 #15660371

order2816
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×#13081819

Splittings

SylowC11 ⋊ C2×#3428

Subgroups

subgroupG/H
centerC22×C4C23×D11
commutatorC2×C11C25×C4
FrattiniC22C25×D11
Fitting, prime radicalC23×C11×#41C2
socleC23×C11C25
cosocleC22×C11C26
hypercenterC23×#41D11
hypocenterC11C2×#3428
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×#41

11534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 1076166);