Finite Group Databasebeta

← Prev (#30633575) Next (#30633577) →

C72×C11×D15 #30633576

order16170
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C2×C72×C11 · Schur multiplier (H2) = C7

Aliases

direct productC72×C11×D15
unambiguous semidirect productC3⋊(C72×D5×C11)
unambiguous semidirect productC5⋊(D3×C72×C11)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C2
derived, HallC3×C5 ⋊ C2×C72×C11
HallC5×C72×C11 ⋊ D3
HallC3×C72×C11 ⋊ D5
HallC3×C5×C72 ⋊ C2×C11
HallC5×C72 ⋊ D3×C11
HallC3×C5×C11 ⋊ C2×C72
HallC3×C72 ⋊ D5×C11
HallC5×C11 ⋊ D3×C72
HallC3×C11 ⋊ C72×D5
SylowC5 ⋊ D3×C72×C11
SylowC3 ⋊ C72×D5×C11

Subgroups

subgroupG/H
center, hypercenterC72×C11D15
commutator, cosocle, hypocenterC3×C5C2×C72×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C2
LCSG ▷ C3×C5
UCSC1 ◁ C72×C11

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

4851 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC72×D11×D15, C7×C11×D7×D15, C7×D15×D77, …
maximal normal subgroup ofC72×D11×D15, C7×C11×D7×D15, C7×D15×D77, …
maximal quotient ofC72×C11×Dic15, C2×C72×C11×D15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 121);