Finite Group Databasebeta

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C3×C31×Dic75 #42124333

order27900
isoclinismisoclinic class of D75
automorphism?
homologyAbelianization (H1) = C3×C4×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×C31×Dic75
unambiguous semidirect productC3⋊(C3×C31×Dic25)

Splittings

derivedC3×C25 ⋊ C3×C4×C31
HallC32×C25×C31 ⋊ C4
HallC25×C31 ⋊ C3×Dic3
HallC32×C31 ⋊ Dic25
HallC32×C25 ⋊ C4×C31
SylowC25 ⋊ C3×Dic3×C31
SylowC32 ⋊ C31×Dic25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C31D75
commutator, hypocenterC3×C25C3×C4×C31
FrattiniC2×C5C3×D15×C31
FittingC2×C32×C25×C31C2
socle, prime radicalC2×C32×C5×C31D5
cosocleC2×C3×C25C2×C3×C31
LCSG ▷ C3×C25
UCSC1 ◁ C2×C3×C31

84 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, 80);