Finite Group Databasebeta

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C3×C31×C3⋊#1039 #42124659

order27900
isoclinismisoclinic class of C3⋊(C5⋊D5)
automorphism?
homologyAbelianization (H1) = C3×C4×C31 · Schur multiplier (H2) = C5

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C3×C31C3⋊(C5⋊D5)
commutator, hypocenterC3×C52C3×C4×C31
FrattiniC2C3×C31×C3⋊(C5⋊D5)
Fitting, socle, prime radicalC2×C32×C52×C31C2
cosocleC2×C3×C52C2×C3×C31
LCSG ▷ C3×C52
UCSC1 ◁ C2×C3×C31

224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 406);