Finite Group Databasebeta

C4×#10622301 #14752157

order2816
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#10622301

Splittings

FittingC42×C8×C11 ⋊ C2
SylowC11 ⋊ C4×#436

Subgroups

subgroupG/H
centerC2×C42C22×D11
commutatorC22×C11C22×C42
FrattiniC22×C4C23×D11
FittingC42×C8×C11C2
socleC23×C11C23×C4
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenterC42×C8D11
hypocenterC11C4×#436
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C42×C8

1254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

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, 167952);