Finite Group Databasebeta

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C2×C52×C11×C19⋊C3 #44535520

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC2×C52×C11×C19⋊C3
unambiguous semidirect product(C2×C19)⋊(C3×C52×C11)
unambiguous semidirect product(C2×C5×C19)⋊(C3×C5×C11)

Splittings

Fitting, socle, HallC2×C52×C11×C19 ⋊ C3
derived, SylowC19 ⋊ C2×C3×C52×C11
HallC52×C11×C19 ⋊ C2×C3
HallC2×C52×C19 ⋊ C3×C11
HallC52×C19 ⋊ C2×C3×C11
HallC2×C11×C19 ⋊ C3×C52
HallC11×C19 ⋊ C2×C3×C52
HallC2×C19 ⋊ C3×C52×C11

Subgroups

subgroupG/H
center, hypercenterC2×C52×C11C19⋊C3
commutator, cosocle, hypocenterC19C2×C3×C52×C11
FrattiniC1G
Fitting, socleC2×C52×C11×C19C3
LCSG ▷ C19
UCSC1 ◁ C2×C52×C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10450

Conjugacy classes & character table

4950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 93);