Finite Group Databasebeta

C22×C22⋊C8×D71 #32860877

order18176
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC22×C22⋊C8×D71

Splittings

FittingC22×C22⋊C8×C71 ⋊ C2
SylowC71 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC23×C4C22×D71
commutatorC2×C71C24×C8
FrattiniC2×C4C24×D71
FittingC22×C22⋊C8×C71C2
socleC24×C71C22×C4
prime radicalC25×D71C4
cosocleC2×C4×C71C25
hypercenterC22×C22⋊C8D71
hypocenterC71C23×C22⋊C8
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

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, 1032993);