Finite Group Databasebeta

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C4×#16811460 #28290706

order13568
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×#16811460

Splittings

FittingC4×2−1+4×C53 ⋊ C2
SylowC53 ⋊ C4×#585

Subgroups

subgroupG/H
centerC2×C4C24×D53
commutatorC2×C53C25×C4
FrattiniC22C25×D53
FittingC4×2−1+4×C53C2
socle, cosocleC22×C53C26
prime radicalC2×#16811460C2
hypercenterC4×2−1+4D53
hypocenterC53C4×#585
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

11346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1076182);