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C3×C72×D5×C11 #30633588

order16170
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C72×C11 · Schur multiplier (H2) = C7

Aliases

direct productC3×C72×D5×C11
unambiguous semidirect productC5⋊(C2×C3×C72×C11)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C72×C11
HallC5×C72×C11 ⋊ C2×C3
HallC3×C5×C72 ⋊ C2×C11
HallC5×C72 ⋊ C2×C3×C11
HallC3×C5×C11 ⋊ C2×C72
HallC5×C11 ⋊ C2×C3×C72
HallC3×C5 ⋊ C2×C72×C11

Subgroups

subgroupG/H
center, hypercenterC3×C72×C11D5
commutator, cosocle, hypocenterC5C2×C3×C72×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C2
LCSG ▷ C5
UCSC1 ◁ C3×C72×C11

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

6468 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C72×C11×AGL(1,𝔽5), C3×C72×C11⋊AGL(1,𝔽5), C3×C7×C11×C7⋊AGL(1,𝔽5), …
maximal normal subgroup ofC3×C72×C11×AGL(1,𝔽5), C3×C72×C11⋊AGL(1,𝔽5), C3×C7×C11×C7⋊AGL(1,𝔽5), …
maximal quotient ofC3×C72×C11×Dic5, C2×C3×C72×D5×C11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 133);