Finite Group Databasebeta

#575×Dic71 #32861539

order18176
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#575×Dic71

Splittings

SylowC71 ⋊ C4×#575

Subgroups

subgroupG/H
centerC2×C4C2×D4×D71
commutatorC4×C71C24×C4
FrattiniC2×C4C24×D71
Fitting, prime radicalC2×#575×C71C2
socleC22×C71C23×D4
cosocleC2×C4×C71C25
hypercenterC2×#575D71
hypocenterC71C4×#575
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

2842 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, 1033655);