Finite Group Databasebeta

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C3×C52×C37⋊C3 #22552275

order8325
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C52×C37⋊C3
unambiguous semidirect productC37⋊(C32×C52)
unambiguous semidirect product(C3×C37)⋊(C3×C52)
unambiguous semidirect product(C5×C37)⋊(C32×C5)
unambiguous semidirect product(C3×C5×C37)⋊(C3×C5)

Splittings

Fitting, socleC3×C52×C37 ⋊ C3
derived, SylowC37 ⋊ C32×C52
HallC52×C37 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C52C37⋊C3
commutator, hypocenterC37C32×C52
FrattiniC1G
Fitting, socleC3×C52×C37C3
LCSG ▷ C37
UCSC1 ◁ C3×C52

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1125 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C52×D37⋊C3, C3×C5×C5⋊(D37⋊C3), C3×C5×D5×C37⋊C3, …
maximal normal subgroup ofC3×C52×D37⋊C3, C3×C5×C5⋊(D37⋊C3), C3×C5×D5×C37⋊C3, …
maximal quotient ofC2×C3×C52×C37⋊C3, C52×A4×C37⋊C3, C3×C52×C22⋊(C37⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8325, 16);