Finite Group Databasebeta

C2×Q8⋊C8×D71 #31963796

order18176
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×Q8⋊C8×D71

Splittings

FittingC2×Q8⋊C8×C71 ⋊ C2
SylowC71 ⋊ C22×Q8⋊C8

Subgroups

subgroupG/H
centerC22×C4D4×D71
commutatorC4×C71C23×C8
FrattiniC42C23×D71
FittingC2×Q8⋊C8×C71C2
socleC23×C71C2×C22⋊C4
prime radicalC23×D71C22⋊C4
cosocleC42×C71C24
hypercenterC2×Q8⋊C8D71
hypocenterC71C22×Q8⋊C8
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 135912);