Finite Group Databasebeta

C4×#10623076 #14912006

order2816
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#10623076

Splittings

FittingC42×D4×C11 ⋊ C2
SylowC11 ⋊ C4×#518

Subgroups

subgroupG/H
centerC22×C4C23×D11
commutatorC2×C11C23×C42
FrattiniC23C24×D11
FittingC42×D4×C11C2
socle, cosocleC23×C11C25
prime radicalC22×D4×D11C22
hypercenterC42×D4D11
hypocenterC11C4×#518
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C42×D4

4186 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, 327801);