Finite Group Databasebeta

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C22×D53⋊#100 #28329250

order13568
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×D53⋊#100
unambiguous semidirect productD53⋊(C22×#100)

Splittings

SylowC53 ⋊ C23×#100

Subgroups

subgroupG/H
centerC23C2×C22⋊#6157
commutatorC22×C53C24×C4
FrattiniC22C24×#6157
FittingC23×D4×C53C4
socleC23×C53C2×C22⋊C4
prime radicalC23×D4×D53C2
cosocleC2×Dic53C25
hypercenterC23×D4#6157
hypocenterC53C23×#100
LCSG ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

7134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1696

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1114726);