Finite Group Databasebeta

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C31×C3⋊(C3⋊#1039) #42124653

order27900
automorphism?
homologyAbelianization (H1) = C4×C31 · Schur multiplier (H2) = C3×C5

Aliases

direct productC31×C3⋊(C3⋊#1039)
unambiguous semidirect productC3⋊(C31×C3⋊#1039)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C31C3⋊(C3⋊(C5⋊D5))
commutator, hypocenterC32×C52C4×C31
FrattiniC2C31×C3⋊(C3⋊(C5⋊D5))
Fitting, socle, prime radicalC2×C32×C52×C31C2
cosocleC2×C32×C52C2×C31
LCSG ▷ C32×C52
UCSC1 ◁ C2×C31

288 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 400);