Finite Group Databasebeta

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C2×#13069534 #14757803

order2816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#13069534

Splittings

FittingC2×C4×C11×C4⋊C4 ⋊ C2
SylowC11 ⋊ C2×#1980

Subgroups

subgroupG/H
centerC22×C4C2×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×C4⋊C4C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#10623008C2
cosocleC22×C4×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11C2×#1980
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

1746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 704

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 173598);