Finite Group Databasebeta

C2×#13068453 #14751603

order2816
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13068453

Splittings

FittingC22×C4×C8×C11 ⋊ C2
SylowC11 ⋊ C2×#1764

Subgroups

subgroupG/H
centerC22×C8D44
commutatorC4×C11C22×C42
FrattiniC22×C4C23×D11
FittingC22×C4×C8×C11C2
socleC23×C11C4×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC22×C4×C8D11
hypocenterC11C2×#1764
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×C4×C8

1558 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

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, 167398);