Finite Group Databasebeta

C22×(C2×D71)⋊C4 #17986446

order4544
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D71)⋊C4

Splittings

FittingC23×C4×C71 ⋊ C2
SylowC71 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D71
commutatorC2×C71C23×C4
FrattiniC22C23×D71
FittingC23×C4×C71C2
socleC24×C71C22
prime radicalC24×D71C2
cosocleC22×C71C24
hypercenterC23×C4D71
hypocenterC71C22×C22⋊C4
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2272

Conjugacy classes & character table

1160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 996);