Finite Group Databasebeta

Q8×C22⋊(C71⋊C8) #32013968

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

Aliases

direct productQ8×C22⋊(C71⋊C8)

Splittings

SylowC71 ⋊ Q8×C22⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC22×C4×Q8×C71C2
socleC23×C71C23×C4
prime radicalC24×C71C22×C4
cosocleC22×C4×C71C24
hypercenterC22×C4×Q8D71
hypocenterC71Q8×C22⋊C8
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

1356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 186084);