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C3×C3⋊#11717961 #20301618

order7380
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊#11717961
unambiguous semidirect productC3⋊(C3×#11717961)

Splittings

Fitting, socle, HallC32×C5×C41 ⋊ C4
derivedC3×C5×C41 ⋊ C3×C4
HallC32×C41 ⋊ AGL(1,𝔽5)
HallC5×C41 ⋊ C3×Dic3
HallC32×C5 ⋊ #4223
SylowC41 ⋊ C3×ΓL(1,𝔽16)
SylowC32 ⋊ #11717961
SylowC5 ⋊ C3×C3⋊#4223

Subgroups

subgroupG/H
center, hypercenterC3C3⋊#11717961
commutator, hypocenterC3×C5×C41C3×C4
FrattiniC1G
Fitting, socleC32×C5×C41C4
LCSG ▷ C3×C5×C41
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

477 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C3⋊#16861480, C3×C3⋊(#11717961⋊C5), C3×C5×C3⋊#11717961, …
maximal normal subgroup ofC3×C3⋊(#11717961⋊C5), C3×C5×C3⋊#11717961
maximal quotient ofC3×C3⋊#16861480, C3×C5×C3⋊#11717961, C3×C3⋊#16861525, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 96);