Finite Group Databasebeta

C2×#13067011 #14720135

order2816
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13067011

Splittings

SylowC11 ⋊ C2×#1479

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC22×C4×Q8×C11C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC42×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11C2×#1479
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×Q8

1282 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 135930);