Finite Group Databasebeta

C22×#17985722 #31963237

order18176
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#17985722

Splittings

FittingC22×C22⋊C8×C71 ⋊ C2
SylowC71 ⋊ C22×#323

Subgroups

subgroupG/H
centerC24(C2×D71)⋊C4
commutatorC22×C71C23×C8
FrattiniC22×C4C23×D71
FittingC22×C22⋊C8×C71C2
socleC24×C71C22⋊C4
prime radicalC25×D71C4
cosocleC22×C4×C71C24
hypercenterC22×C22⋊C8D71
hypocenterC71C22×#323
LCSG ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

2878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

2888 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 135353);