Finite Group Databasebeta

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C3×C5×C7×C61⋊C5 #44545060

order32025
automorphism?
homologyAbelianization (H1) = C3×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C7×C61⋊C5
unambiguous semidirect product(C3×C61)⋊(C52×C7)
unambiguous semidirect product(C3×C5×C61)⋊(C5×C7)
unambiguous semidirect product(C3×C7×C61)⋊C52
unambiguous semidirect product(C3×C5×C7×C61)⋊C5

Splittings

Fitting, socleC3×C5×C7×C61 ⋊ C5
derived, SylowC61 ⋊ C3×C52×C7
HallC3×C7×C61 ⋊ C52
HallC7×C61 ⋊ C3×C52
HallC3×C61 ⋊ C52×C7

Subgroups

subgroupG/H
center, hypercenterC3×C5×C7C61⋊C5
commutator, cosocle, hypocenterC61C3×C52×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C61C5
LCSG ▷ C61
UCSC1 ◁ C3×C5×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6405

Conjugacy classes & character table

1785 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32025, 16);