Finite Group Databasebeta

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C3×C25×Dic51 #29505656

order15300
isoclinismisoclinic class of D51
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×Dic51
unambiguous semidirect productC3⋊(C3×C25×Dic17)

Splittings

derivedC3×C17 ⋊ C3×C4×C25
HallC32×C17×C25 ⋊ C4
HallC17×C25 ⋊ C3×Dic3
HallC32×C25 ⋊ Dic17
HallC32×C17 ⋊ C4×C25
SylowC17 ⋊ C3×Dic3×C25
SylowC32 ⋊ C25×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D51
commutator, hypocenterC3×C17C3×C4×C25
FrattiniC2×C5C3×C5×D51
FittingC2×C32×C17×C25C2
socle, prime radicalC2×C32×C5×C17C2×C5
cosocleC2×C3×C5×C17C2×C3×C5
LCSG ▷ C3×C17
UCSC1 ◁ C2×C3×C25

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5100

Conjugacy classes & character table

4050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 42);