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C3×C71×C52⋊C3 #30630428

order15975
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C32×C71 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C71×C52⋊C3
unambiguous semidirect productC52⋊(C32×C71)
unambiguous semidirect product(C3×C52)⋊(C3×C71)
unambiguous semidirect product(C52×C71)⋊C32
unambiguous semidirect product(C3×C52×C71)⋊C3

Splittings

Fitting, socleC3×C52×C71 ⋊ C3
derived, SylowC52 ⋊ C32×C71
HallC52×C71 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C71C52⋊C3
commutator, cosocle, hypocenterC52C32×C71
FrattiniC1G
Fitting, socleC3×C52×C71C3
LCSG ▷ C52
UCSC1 ◁ C3×C71

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3195

Conjugacy classes & character table

2343 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofC3⋊(C71⋊#3874)
maximal subgroup ofC3×C52⋊C3×D71, C3×C71×#3874, C3×C71⋊#3874, …
maximal normal subgroup ofC3×C52⋊C3×D71, C3×C71×#3874, C3×C71⋊#3874, …
maximal quotient ofC2×C3×C71×C52⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15975, 10);