Finite Group Databasebeta

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C4×#10622450 #14751672

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

Aliases

direct productC4×#10622450

Splittings

FittingC4×C11×C4⋊C8 ⋊ C2
SylowC11 ⋊ C4×#423

Subgroups

subgroupG/H
centerC2×C42C22×D11
commutatorC22×C11C22×C42
FrattiniC22×C4C23×D11
FittingC4×C11×C4⋊C8C2
socleC23×C11C23×C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenterC4×C4⋊C8D11
hypocenterC11C4×#423
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1382 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, 167467);