Finite Group Databasebeta

C4×#17985982 #31995128

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

Aliases

direct productC4×#17985982

Splittings

FittingC4×#101×C71 ⋊ C2
SylowC71 ⋊ C4×#413

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D71
commutatorC22×C71C22×C42
FrattiniC22×C4C23×D71
FittingC4×#101×C71C2
socleC22×C71C22×C22⋊C4
prime radicalC22×#11765866C22
cosocleC22×C4×C71C24
hypercenterC4×#101D71
hypocenterC71C4×#413
LCSG ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

1570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 167244);