Finite Group Databasebeta

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C4×#10622121 #14644368

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

Aliases

direct productC4×#10622121

Splittings

FittingC4×C11×C4⋊C8 ⋊ C2
SylowC11 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC2×C42C22⋊D11
commutatorC4×C11C2×C4×C8
FrattiniC2×C42C22×D11
FittingC4×C11×C4⋊C8C2
socleC23×C11C2×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenterC4×C4⋊C8D11
hypocenterC11C4×D4⋊C8
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C43 ◁ C4×C4⋊C8

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

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, 60163);