Finite Group Databasebeta

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C3×C49⋊(Dic11⋊C5) #44568320

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49⋊(Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C3×Dic49)
unambiguous semidirect product(C3×Dic539)⋊C5

Splittings

derived, HallC11×C49 ⋊ C3×C4×C5
HallC3×C49×C11⋊C5 ⋊ C4
HallC3×Dic539 ⋊ C5
HallC49×C11⋊C5 ⋊ C3×C4
HallDic539 ⋊ C3×C5
HallC3×C11×C49 ⋊ C4×C5
HallC3×C11⋊C5 ⋊ Dic49
HallC3×C49 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3×Dic49
SylowC49 ⋊ C3×Dic11⋊C5
HallC3×C11 ⋊ C5×Dic49
SylowC11 ⋊ C3×C5×Dic49

Subgroups

subgroupG/H
center, hypercenterC2×C3C49⋊AGL(1,𝔽11)
commutator, hypocenterC11×C49C3×C4×C5
FrattiniC2×C7C3×C7⋊AGL(1,𝔽11)
FittingC2×C3×C11×C49C2×C5
socleC2×C3×C7×C11C5×D7
prime radicalC2×C3×C7×C11⋊C5D7
cosocleC2×C11×C49C2×C3×C5
LCSG ▷ C11×C49
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6468

Conjugacy classes & character table

1074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 22);