Finite Group Databasebeta

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C3×C25×D69 #23780340

order10350
isoclinismisoclinic class of D69
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×D69
unambiguous semidirect productC3⋊(C3×C25×D23)
unambiguous semidirect productC23⋊(C3×D3×C25)

Splittings

Fitting, HallC32×C23×C25 ⋊ C2
derivedC3×C23 ⋊ C2×C3×C25
HallC23×C25 ⋊ C3×D3
HallC32×C25 ⋊ D23
HallC32×C23 ⋊ C2×C25
SylowC23 ⋊ C3×D3×C25
SylowC32 ⋊ C25×D23

Subgroups

subgroupG/H
center, hypercenterC3×C25D69
commutator, hypocenterC3×C23C2×C3×C25
FrattiniC5C3×C5×D69
FittingC32×C23×C25C2
socleC32×C5×C23C2×C5
prime radicalC3×C5×D69C5
cosocleC3×C5×C23C2×C3×C5
LCSG ▷ C3×C23
UCSC1 ◁ C3×C25

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2700 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D3×C25×D23, C3×D25×D69, C3×D69⋊D25, …
maximal normal subgroup ofC3×D3×C25×D23, C3×D25×D69, C3×D69⋊D25, …
maximal quotient ofC3×C25×Dic69, C2×C3×C25×D69

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10350, 14);