Finite Group Databasebeta

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C2×C19⋊C3×C11⋊C25 #44535431

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×C19⋊C3×C11⋊C25
unambiguous semidirect product(C2×C11)⋊(C25×C19⋊C3)
unambiguous semidirect product(C2×C19)⋊(C3×C11⋊C25)
unambiguous semidirect product(C2×C11×C19⋊C3)⋊C25
unambiguous semidirect product(C2×C19×C11⋊C25)⋊C3

Splittings

derived, HallC11×C19 ⋊ C2×C3×C25
HallC2×C19×C11⋊C25 ⋊ C3
HallC19×C11⋊C25 ⋊ C2×C3
HallC2×C11×C19⋊C3 ⋊ C25
HallC11×C19⋊C3 ⋊ C2×C25
HallC2×C11×C19 ⋊ C3×C25
HallC2×C19 ⋊ C3×C11⋊C25
HallC2×C11 ⋊ C25×C19⋊C3
SylowC19 ⋊ C2×C3×C11⋊C25
SylowC11 ⋊ C2×C25×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊C5×C19⋊C3
commutator, hypocenterC11×C19C2×C3×C25
FrattiniC5C2×C11⋊C5×C19⋊C3
Fitting, socleC2×C5×C11×C19C3×C5
prime radicalC2×C5×C11×C19⋊C3C5
cosocleC5×C11×C19C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10450

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 4);