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C5×C11⋊((C49⋊C3)⋊C4) #44568327

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

Aliases

direct productC5×C11⋊((C49⋊C3)⋊C4)
unambiguous semidirect product(C49⋊C3)⋊(C5×Dic11)
unambiguous semidirect product(C5×Dic539)⋊C3

Splittings

derived, HallC11×C49 ⋊ C3×C4×C5
HallC5×Dic539 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C4
HallC5×C11×C49 ⋊ C3×C4
HallDic539 ⋊ C3×C5
HallC11×C49⋊C3 ⋊ C4×C5
HallC5×C49⋊C3 ⋊ Dic11
HallC5×C49 ⋊ C3×Dic11
HallC49⋊C3 ⋊ C5×Dic11
HallC5×C11 ⋊ (C49⋊C3)⋊C4
SylowC49 ⋊ C3×C5×Dic11
SylowC11 ⋊ C5×(C49⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊(D49⋊C3)
commutator, hypocenterC11×C49C3×C4×C5
FrattiniC2×C7C5×C11⋊AGL(1,𝔽7)
FittingC2×C5×C11×C49C2×C3
socleC2×C5×C7×C11AGL(1,𝔽7)
prime radicalC2×C5×C11×C49⋊C3C2
cosocleC2×C11×C49C2×C3×C5
LCSG ▷ C11×C49
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10780

Conjugacy classes & character table

1090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 29);