Finite Group Databasebeta

C4⋊C8×D71 #17986018

order4544
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC4⋊C8×D71

Splittings

FittingC4⋊C8×C71 ⋊ C2
SylowC71 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D71
commutatorC2×C71C22×C8
FittingC4⋊C8×C71C2
socleC22×C71C22×C4
prime radicalC22×D71C2×C4
cosocleC2×C4×C71C23
hypercenterC4⋊C8D71
hypocenterC71C2×C4⋊C8
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2272

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 568);