Finite Group Databasebeta

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C22×#16811574 #28328653

order13568
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16811574
unambiguous semidirect productD53⋊(C2×#389)

Splittings

FittingC22×C4⋊C4×C53 ⋊ C4
SylowC53 ⋊ C22×#389

Subgroups

subgroupG/H
centerC24C22×#6157
commutatorC22×C53C24×C4
FrattiniC22C24×#6157
FittingC22×C4⋊C4×C53C4
socleC24×C53C22×C4
prime radicalC24×D53C23
cosocleC22×D53C25
hypercenterC22×C4⋊C4#6157
hypocenterC53C22×#389
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×C4⋊C4

4894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1114129);