Finite Group Databasebeta

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C31×C3⋊#64480 #42124783

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

Aliases

direct productC31×C3⋊#64480
unambiguous semidirect productC3⋊(C31×#64480)

Splittings

Fitting, socleC3×C52×C31 ⋊ Dic3
derived, HallC3×C52⋊C3 ⋊ C4×C31
HallC3×C31×C52⋊C3 ⋊ C4
HallC52×C31 ⋊ C3⋊Dic3
SylowC52 ⋊ C31×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC31C3⋊#64480
commutator, hypocenterC3×C52⋊C3C4×C31
FrattiniC1G
Fitting, socleC3×C52×C31Dic3
prime radicalC3×C31×(C5⋊D5)⋊C3C2
cosocleC3×(C5⋊D5)⋊C3C2×C31
LCSG ▷ C3×C52⋊C3
UCSC1 ◁ C31

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

558 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 530);