Finite Group Databasebeta

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C2×C5×D409⋊C3 #37589349

order24540
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D409⋊C3
unambiguous semidirect productD409⋊(C2×C3×C5)
unambiguous semidirect product(C409⋊C3)⋊(C22×C5)
unambiguous semidirect product(C2×D409)⋊(C3×C5)
unambiguous semidirect product(C2×C409⋊C3)⋊(C2×C5)
unambiguous semidirect product(C2×C5×D409)⋊C3

Splittings

Fitting, socleC2×C5×C409 ⋊ C2×C3
derived, SylowC409 ⋊ C22×C3×C5
HallC2×C5×D409 ⋊ C3
HallC5×C409⋊C3 ⋊ C22
HallC5×C409 ⋊ C22×C3
HallC2×D409 ⋊ C3×C5
HallC409⋊C3 ⋊ C22×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5D409⋊C3
commutator, cosocle, hypocenterC409C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C409C2×C3
LCSG ▷ C409
UCSC1 ◁ C2×C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4090

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24540, 21);