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C23×C5⋊(D49⋊C3) #46798919

order33810
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C5⋊(D49⋊C3)
unambiguous semidirect productC5⋊(C23×D49⋊C3)
unambiguous semidirect product(C49⋊C3)⋊(D5×C23)
unambiguous semidirect productD245⋊(C3×C23)
unambiguous semidirect product(C23×D245)⋊C3

Splittings

Fitting, HallC5×C23×C49 ⋊ C2×C3
derived, HallC5×C49 ⋊ C2×C3×C23
HallC5×C23×C49⋊C3 ⋊ C2
HallC23×D245 ⋊ C3
HallC23×C49⋊C3 ⋊ D5
HallC23×C49 ⋊ C3×D5
HallC5×C49⋊C3 ⋊ C2×C23
HallD245 ⋊ C3×C23
HallC49⋊C3 ⋊ D5×C23
HallC5×C23 ⋊ D49⋊C3
SylowC49 ⋊ C3×D5×C23
SylowC5 ⋊ C23×D49⋊C3

Subgroups

subgroupG/H
center, hypercenterC23C5⋊(D49⋊C3)
commutator, cosocle, hypocenterC5×C49C2×C3×C23
FrattiniC7C23×C5⋊AGL(1,𝔽7)
FittingC5×C23×C49C2×C3
socleC5×C7×C23AGL(1,𝔽7)
LCSG ▷ C5×C49
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5635

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33810, 23);