Finite Group Databasebeta

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C2×C5×C19⋊C32 #44570571

order32490
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC2×C5×C19⋊C32
unambiguous semidirect product(C2×C19×C19⋊C3)⋊(C3×C5)
unambiguous semidirect product(C2×#11762246)⋊(C3×C5)
unambiguous semidirect product(C2×C5×#11762245)⋊C3
unambiguous semidirect product(C2×C5×C19×C19⋊C3)⋊C3
unambiguous semidirect product(C2×C5×#11762246)⋊C3

Splittings

Fitting, socle, HallC2×C5×C192 ⋊ C32
derived, SylowC192 ⋊ C2×C32×C5
HallC5×C192 ⋊ C2×C32
HallC2×C192 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5C19⋊C32
commutator, cosocle, hypocenterC192C2×C32×C5
FrattiniC1G
Fitting, socleC2×C5×C192C32
LCSG ▷ C192
UCSC1 ◁ C2×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 570

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 155);