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C5×C7×D61⋊C5 #36319449

order21350
automorphism?
homologyAbelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7×D61⋊C5
unambiguous semidirect productD61⋊(C52×C7)
unambiguous semidirect product(C61⋊C5)⋊(C2×C5×C7)
unambiguous semidirect product(C5×D61)⋊(C5×C7)
unambiguous semidirect product(C7×D61)⋊C52
unambiguous semidirect product(C5×C7×D61)⋊C5

Splittings

Fitting, socleC5×C7×C61 ⋊ C2×C5
derived, SylowC61 ⋊ C2×C52×C7
HallC5×C7×C61⋊C5 ⋊ C2
HallC5×C61⋊C5 ⋊ C2×C7
HallC7×D61 ⋊ C52
HallC7×C61 ⋊ C2×C52
HallD61 ⋊ C52×C7

Subgroups

subgroupG/H
center, hypercenterC5×C7D61⋊C5
commutator, cosocle, hypocenterC61C2×C52×C7
FrattiniC1G
Fitting, socleC5×C7×C61C2×C5
LCSG ▷ C61
UCSC1 ◁ C5×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2135

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21350, 14);