Finite Group Databasebeta

← Prev (#44439985) Next (#44439987) →

C4×C5×#13091812 #44439986

order29340
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×#13091812

Splittings

derived, SylowC163 ⋊ C4×C5×C9
HallC4×C5×C163 ⋊ C9
HallC5×C163 ⋊ C4×C9
HallC4×C163 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5C163⋊C3
commutator, hypocenterC163C4×C5×C9
FrattiniC2×C3C2×C5×C163⋊C3
FittingC3×C4×C5×C163C3
socle, prime radicalC2×C3×C5×C163C2×C3
cosocleC2×C3×C163C2×C3×C5
LCSG ▷ C163
UCSC1 ◁ C3×C4×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29340

Conjugacy classes & character table

3420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29340, 2);