Finite Group Databasebeta

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C2×C3×#11762245⋊C5 #44570559

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

Aliases

direct productC2×C3×#11762245⋊C5
unambiguous semidirect product(C2×C192⋊C5)⋊C32
unambiguous semidirect product(C2×C3×#11762245)⋊C5
unambiguous semidirect product(C2×C3×C192⋊C5)⋊C3

Splittings

Fitting, socleC2×C3×C192 ⋊ C3×C5
derived, SylowC192 ⋊ C2×C32×C5
HallC2×C3×#11762245 ⋊ C5
HallC2×C192⋊C5 ⋊ C32
HallC3×#11762245 ⋊ C2×C5
HallC192⋊C5 ⋊ C2×C32
HallC2×C192 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3#11762245⋊C5
commutator, cosocle, hypocenterC192C2×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C192C3×C5
LCSG ▷ C192
UCSC1 ◁ C2×C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 570

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32490, 143);