Finite Group Databasebeta

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C5×C7×(C61⋊C3)⋊C5 #44545056

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

Aliases

direct productC5×C7×(C61⋊C3)⋊C5
unambiguous semidirect product(C61⋊C3)⋊(C52×C7)
unambiguous semidirect product(C61⋊C5)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C61⋊C3)⋊(C5×C7)
unambiguous semidirect product(C7×C61⋊C3)⋊C52
unambiguous semidirect product(C5×C61⋊C5)⋊(C3×C7)
unambiguous semidirect product(C5×C7×C61⋊C3)⋊C5

Splittings

Fitting, socleC5×C7×C61 ⋊ C3×C5
derived, SylowC61 ⋊ C3×C52×C7
HallC5×C7×C61⋊C5 ⋊ C3
HallC5×C61⋊C5 ⋊ C3×C7
HallC7×C61⋊C3 ⋊ C52
HallC7×C61 ⋊ C3×C52
HallC61⋊C3 ⋊ C52×C7

Subgroups

subgroupG/H
center, hypercenterC5×C7(C61⋊C3)⋊C5
commutator, cosocle, hypocenterC61C3×C52×C7
FrattiniC1G
Fitting, socleC5×C7×C61C3×C5
LCSG ▷ C61
UCSC1 ◁ C5×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2135

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32025, 12);