Finite Group Databasebeta

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C4×#16811434 #28248321

order13568
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#16811434

Splittings

FittingC4×H(5,𝔽2)×C53 ⋊ C2
SylowC53 ⋊ C4×#577

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC4×C53C24×C4
FrattiniC2×C4C24×D53
FittingC4×H(5,𝔽2)×C53C2
socleC22×C53C23×D4
prime radicalC2×#16811434C2
cosocleC2×C4×C53C25
hypercenterC4×H(5,𝔽2)D53
hypocenterC53C4×#577
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×H(5,𝔽2)

2742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

1856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1033797);