Finite Group Databasebeta

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C5×C11×C49⋊C9 #37564673

order24255
automorphism?
homologyAbelianization (H1) = C5×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C49⋊C9
unambiguous semidirect productC49⋊(C5×C9×C11)
unambiguous semidirect product(C5×C49)⋊(C9×C11)
unambiguous semidirect product(C5×C11×C49)⋊C9

Splittings

derived, SylowC49 ⋊ C5×C9×C11
HallC5×C11×C49 ⋊ C9
HallC11×C49 ⋊ C5×C9
HallC5×C49 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11C49⋊C3
commutator, hypocenterC49C5×C9×C11
FrattiniC3×C7C5×C11×ΓL(1,𝔽8)
FittingC3×C5×C11×C49C3
socle, prime radicalC3×C5×C7×C11ΓL(1,𝔽8)
cosocleC3×C49C3×C5×C11
LCSG ▷ C49
UCSC1 ◁ C3×C5×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24255

Conjugacy classes & character table

3135 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24255, 4);