Finite Group Databasebeta

D4×C71⋊#95 #31918922

order18176
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productD4×C71⋊#95

Splittings

SylowC71 ⋊ D4×#95

Subgroups

subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC22×C4×D4×C71C2
socle, cosocleC24×C71C24
prime radicalC23×D4×C71C22
hypercenterC22×C4×D4D71
hypocenterC71D4×#95
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C4×D4

3562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 91038);