Finite Group Databasebeta

← Prev (#29505656) Next (#29505658) →

C3×C17×Dic75 #29505657

order15300
isoclinismisoclinic class of D75
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×Dic75
unambiguous semidirect productC3⋊(C3×C17×Dic25)

Splittings

derivedC3×C25 ⋊ C3×C4×C17
HallC32×C17×C25 ⋊ C4
HallC17×C25 ⋊ C3×Dic3
HallC32×C25 ⋊ C4×C17
HallC32×C17 ⋊ Dic25
SylowC25 ⋊ C3×Dic3×C17
SylowC32 ⋊ C17×Dic25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D75
commutator, hypocenterC3×C25C3×C4×C17
FrattiniC2×C5C3×C17×D15
FittingC2×C32×C17×C25C2
socle, prime radicalC2×C32×C5×C17D5
cosocleC2×C3×C25C2×C3×C17
LCSG ▷ C3×C25
UCSC1 ◁ C2×C3×C17

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5100

Conjugacy classes & character table

3978 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 43);