Finite Group Databasebeta

C22×C4×C22⋊#6157 #28328616

order13568
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×C4×C22⋊#6157

Splittings

FittingC24×C4×C53 ⋊ C4
SylowC53 ⋊ C22×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×#6157
commutatorC2×C53C23×C42
FrattiniC22C24×#6157
FittingC24×C4×C53C4
socleC24×C53C22×C4
prime radicalC25×D53C22
cosocleC22×D53C25
hypercenterC24×C4#6157
hypocenterC53C22×C4×C22⋊C4
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C23×C4 ◁ C24×C4

9534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1114092);