Finite Group Databasebeta

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C4×#16811493 #28306375

order13568
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct productC4×#16811493

Splittings

FittingC4×C4⋊C4×C53 ⋊ C4
SylowC53 ⋊ C4×#339

Subgroups

subgroupG/H
centerC22×C4C22⋊#6157
commutatorC4×C53C43
FrattiniC22×C4C22×#6157
FittingC4×C4⋊C4×C53C4
socleC23×C53C2×C22⋊C4
prime radicalC23×D53C2×D4
cosocleC22×C4×D53C23
hypercenterC4×C4⋊C4#6157
hypocenterC53C4×#339
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

1214 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, 1091851);