Finite Group Databasebeta

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C3×C3⋊(C31⋊#1039) #42124658

order27900
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C5

Aliases

direct productC3×C3⋊(C31⋊#1039)
unambiguous semidirect productC3⋊(C3×C31⋊#1039)

Splittings

derivedC3×C52×C31 ⋊ C3×C4
HallC32×C52×C31 ⋊ C4
HallC52×C31 ⋊ C3×Dic3
HallC32×C31 ⋊ #1039
HallC32×C52 ⋊ Dic31
SylowC31 ⋊ C3×C3⋊#1039
SylowC52 ⋊ C3×Dic93
SylowC32 ⋊ C31⋊#1039

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C5⋊D155)
commutator, hypocenterC3×C52×C31C3×C4
FrattiniC2C3×C3⋊(C5⋊D155)
Fitting, socle, prime radicalC2×C32×C52×C31C2
cosocleC2×C3×C52×C31C2×C3
LCSG ▷ C3×C52×C31
UCSC1 ◁ C2×C3

224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6984 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 405);