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C3×C41×C52⋊C3 #22604338

order9225
isoclinismisoclinic class of C52⋊C3
automorphism?
homologyAbelianization (H1) = C32×C41 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C41×C52⋊C3
unambiguous semidirect productC52⋊(C32×C41)
unambiguous semidirect product(C3×C52)⋊(C3×C41)
unambiguous semidirect product(C52×C41)⋊C32
unambiguous semidirect product(C3×C52×C41)⋊C3

Splittings

Fitting, socleC3×C52×C41 ⋊ C3
derived, SylowC52 ⋊ C32×C41
HallC52×C41 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C41C52⋊C3
commutator, hypocenterC52C32×C41
FrattiniC1G
Fitting, socleC3×C52×C41C3
LCSG ▷ C52
UCSC1 ◁ C3×C41

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1353 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofC3⋊(C41⋊#3874), C3⋊#27134196, C3⋊#27134237, …
maximal subgroup ofC3×C41×#3874, C3×C41⋊#3874, C3×C41×(C5⋊D5)⋊C3, …
maximal normal subgroup ofC3×C41×#3874, C3×C41⋊#3874, C3×C41×(C5⋊D5)⋊C3, …
maximal quotient ofC2×C3×C41×C52⋊C3, A4×C41×C52⋊C3, C3×C41×C22⋊(C52⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9225, 10);