Finite Group Databasebeta

← Prev (#22552272) Next (#22552274) →

C3×C52⋊(C37⋊C3) #22552273

order8325
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C3×C5

Aliases

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

Splittings

Fitting, socleC3×C52×C37 ⋊ C3
derived, HallC52×C37 ⋊ C32
SylowC37 ⋊ C3×C52⋊C3
SylowC52 ⋊ C3×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C52⋊(C37⋊C3)
commutator, hypocenterC52×C37C32
FrattiniC1G
Fitting, socleC3×C52×C37C3
LCSG ▷ C52×C37
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

933 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#19149851, C3×(C5⋊D5)⋊(C37⋊C3), C3×D37⋊(C52⋊C3), …
maximal normal subgroup ofC3×#19149851, C3×(C5⋊D5)⋊(C37⋊C3), C3×D37⋊(C52⋊C3), …
maximal quotient ofC2×C3×C52⋊(C37⋊C3), A4×C52⋊(C37⋊C3), C3×C22⋊(C52⋊(C37⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8325, 14);