Finite Group Databasebeta

C22×C22⋊Q8×D71 #32904091

order18176
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×C22⋊Q8×D71

Splittings

FittingC22×C22⋊Q8×C71 ⋊ C2
SylowC71 ⋊ C23×C22⋊Q8

Subgroups

subgroupG/H
centerC24C23×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC25×D71C22
hypercenterC22×C22⋊Q8D71
hypocenterC71C23×C22⋊Q8
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

14078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

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, 1076207);