Finite Group Databasebeta

C22×Q8×C71⋊C8 #32861804

order18176
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×C71⋊C8

Splittings

SylowC71 ⋊ C22×C8×Q8

Subgroups

subgroupG/H
centerC23×C4C22×D71
commutatorC2×C71C24×C8
FrattiniC2×C4C24×D71
FittingC22×C4×Q8×C71C2
socle, prime radicalC24×C71C22×C4
cosocleC2×C4×C71C25
hypercenterC22×C4×Q8D71
hypocenterC71C22×C8×Q8
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

2478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1033920);