Finite Group Databasebeta

C2×C22⋊(C71⋊C8) #17985960

order4544
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊(C71⋊C8)

Splittings

SylowC71 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D71
commutatorC2×C71C22×C8
FrattiniC2×C4C22×D71
FittingC23×C4×C71C2
socleC23×C71C2×C4
prime radicalC24×C71C4
cosocleC2×C4×C71C23
hypercenterC23×C4D71
hypocenterC71C2×C22⋊C8
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C23×C4

202 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, 510);