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C2×#20290562 #28318990

order13568
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#20290562
unambiguous semidirect productD53⋊#1793

Splittings

FittingC2×2−1+4×C53 ⋊ C4
SylowC53 ⋊ C2×#1793

Subgroups

subgroupG/H
centerC22#16811564
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC2×2−1+4×C53C4
socleC22×C53#379
prime radicalC2×2−1+4×D53C2
cosocleC2×C4×D53C24
hypercenterC2×2−1+4#6157
hypocenterC53C2×#1793
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

3682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1696

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1104466);