Finite Group Databasebeta

C2×#13069173 #14755815

order2816
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#13069173

Splittings

SylowC11 ⋊ C2×#1916

Subgroups

subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C23×C8
FrattiniC22×C4C23×D11
FittingC22×C4×C8×C11C2
socle, prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenterC22×C4×C8D11
hypocenterC11C2×#1916
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C4×C8

1134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2816

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 171610);