Finite Group Databasebeta

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C4×#10622149 #14669092

order2816
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#10622149

Splittings

SylowC11 ⋊ C4×#364

Subgroups

subgroupG/H
centerC4×C8C22⋊D11
commutatorC4×C11C2×C4×C8
FrattiniC22×C8C22×D11
FittingC4×C11×M32C2
socleC22×C11C2×C4⋊C8
prime radicalC23×C11C2×M16
cosocleC22×C8×C11C23
hypercenterC4×M32D11
hypocenterC11C4×#364
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4×C8 ◁ C2×C4×C8 ◁ C4×M32

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 84887);