Finite Group Databasebeta

C2×#13070502 #14907179

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13070502

Splittings

SylowC11 ⋊ C2×#2179

Subgroups

subgroupG/H
centerC2×C4D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
Fitting, prime radicalC2×C11×#508C2
socleC22×C11C4×D8
cosocleC2×C8×C11C24
hypercenterC2×#508D11
hypocenterC11C2×#2179
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C2×#508

654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 322974);