Finite Group Databasebeta

#459×Dic71 #32003629

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#459×Dic71

Splittings

SylowC71 ⋊ C4×#459

Subgroups

subgroupG/H
centerC23C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC2×#459×C71C2
socleC23×C71C22×D4
cosocleC22×C4×C71C24
hypercenterC2×#459D71
hypocenterC71C4×#459
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

1272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 175745);