Finite Group Databasebeta

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C4⋊C4×C4⋊#6157 #28312797

order13568
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4⋊C4×C4⋊#6157

Splittings

FittingC4×C4⋊C4×C53 ⋊ C4
SylowC53 ⋊ C4⋊C42

Subgroups

subgroupG/H
center, FrattiniC23C23×#6157
commutatorC22×C53C22×C42
FittingC4×C4⋊C4×C53C4
socleC23×C53C23×C4
prime radical, cosocleC23×D53C24
hypercenterC4×C4⋊C4#6157
hypocenterC53C4⋊C42
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C4⋊C4

1838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1098273);