Finite Group Databasebeta

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C4×#10622166 #14644279

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

Aliases

direct productC4×#10622166

Splittings

SylowC11 ⋊ C4×#324

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic11
commutatorC22×C11C2×C4×C8
FrattiniC23×C4C22×D11
FittingC2×C4×C11×C4⋊C4C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22×C4
cosocleC23×C4×C11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C4×#324
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1408

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, 60074);