Finite Group Databasebeta

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C3×C3⋊#16810010 #44478259

order30420
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C3⋊#16810010
unambiguous semidirect productC3⋊(C3×#16810010)

Splittings

Fitting, socle, HallC32×C5×C132 ⋊ C4
derivedC3×C5×C132 ⋊ C3×C4
HallC32×C132 ⋊ Dic5
HallC5×C132 ⋊ C3×Dic3
SylowC132 ⋊ C3×Dic15
HallC32×C5 ⋊ #10621728
SylowC32 ⋊ #16810010
SylowC5 ⋊ C3×C3⋊#10621728

Subgroups

subgroupG/H
center, hypercenterC3C3⋊#16810010
commutator, hypocenterC3×C5×C132C3×C4
FrattiniC1G
Fitting, socleC32×C5×C132C4
prime radicalC32×C5×C13⋊D13C2
cosocleC3×C5×C13⋊D13C2×C3
LCSG ▷ C3×C5×C132
UCSC1 ◁ C3

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5070

Conjugacy classes & character table

1944 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 848);