Finite Group Databasebeta

C4×#17986109 #31995934

order18176
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#17986109

Splittings

FittingC42×D4×C71 ⋊ C2
SylowC71 ⋊ C4×#442

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D71
commutatorC4×C71C22×C42
FrattiniC22×C4C23×D71
FittingC42×D4×C71C2
socleC23×C71C22×D4
prime radicalC22×#11765850C22
cosocleC22×C4×C71C24
hypercenterC42×D4D71
hypocenterC71C4×#442
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C43 ◁ C42×D4

1326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2888 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 168050);