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C2×C41×D49⋊C3 #37563010

order24108
automorphism?
homologyAbelianization (H1) = C22×C3×C41 · Schur multiplier (H2) = C2

Aliases

direct productC2×C41×D49⋊C3
unambiguous semidirect productD49⋊(C2×C3×C41)
unambiguous semidirect product(C49⋊C3)⋊(C22×C41)
unambiguous semidirect product(C2×D49)⋊(C3×C41)
unambiguous semidirect product(C2×C49⋊C3)⋊(C2×C41)
unambiguous semidirect product(C2×C41×D49)⋊C3

Splittings

FittingC2×C41×C49 ⋊ C2×C3
derived, SylowC49 ⋊ C22×C3×C41
HallC2×C41×D49 ⋊ C3
HallC41×C49⋊C3 ⋊ C22
HallC41×C49 ⋊ C22×C3
HallC2×D49 ⋊ C3×C41
HallC49⋊C3 ⋊ C22×C41

Subgroups

subgroupG/H
center, hypercenterC2×C41D49⋊C3
commutator, cosocle, hypocenterC49C22×C3×C41
FrattiniC7C2×C41×AGL(1,𝔽7)
FittingC2×C41×C49C2×C3
socleC2×C7×C41AGL(1,𝔽7)
LCSG ▷ C49
UCSC1 ◁ C2×C41

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4018

Conjugacy classes & character table

1148 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24108, 17);