Finite Group Databasebeta

C8×(C2×D71)⋊C8 #31887918

order18176
automorphism?
homologyAbelianization (H1) = C2×C82 · Schur multiplier (H2) = C23×C8

Aliases

direct productC8×(C2×D71)⋊C8

Splittings

FittingC2×C82×C71 ⋊ C2
SylowC71 ⋊ C8×C22⋊C8

Subgroups

subgroupG/H
centerC2×C4×C8C2×D71
commutatorC2×C71C2×C82
FrattiniC2×C42C22×D71
FittingC2×C82×C71C2
socleC23×C71C2×C42
prime radicalC23×D71C42
cosocleC2×C42×C71C23
hypercenterC2×C82D71
hypocenterC71C8×C22⋊C8
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4×C8 ◁ C2×C82

726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

4640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 60034);