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C22⋊C4×#11719936 #28318119

order13568
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22⋊C4×#11719936

Splittings

SylowC53 ⋊ C22⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC23C23×#6157
commutatorC22×C53C22×C42
FittingC4×C22⋊C4×C53C4
socleC23×C53C23×C4
prime radicalC24×D53C2×C4
cosocleC22×Dic53C24
hypercenterC4×C22⋊C4#6157
hypocenterC53C22⋊C4×M16
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4

1774 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, 1103595);