Finite Group Databasebeta

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C4×#10622106 #14644276

order2816
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#10622106

Splittings

FittingC4×C11×C22⋊C8 ⋊ C2
SylowC11 ⋊ C4×#323

Subgroups

subgroupG/H
centerC22×C4(C2×D11)⋊C4
commutatorC22×C11C2×C4×C8
FrattiniC23×C4C22×D11
FittingC4×C11×C22⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC23×C4×C11C23
hypercenterC4×C22⋊C8D11
hypocenterC11C4×#323
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 60071);