Finite Group Databasebeta

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C2×#20291223 #28328740

order13568
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#20291223
unambiguous semidirect productD53⋊#2344

Splittings

FittingC22×C4⋊C4×C53 ⋊ C4
SylowC53 ⋊ C2×#2344

Subgroups

subgroupG/H
centerC23C23×#6157
commutatorC22×C53C24×C4
FrattiniC22C24×#6157
FittingC22×C4⋊C4×C53C4
socleC23×C53C23×C4
prime radicalC24×D53C23
cosocleC22×D53C25
hypercenterC22×C4⋊C4#6157
hypocenterC53C2×#2344
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×C4⋊C4

3526 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, 1114216);