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C5×C11⋊((C31⋊C3)⋊C4) #35205654

order20460
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊((C31⋊C3)⋊C4)
unambiguous semidirect product(C5×Dic341)⋊C3

Splittings

derived, HallC11×C31 ⋊ C3×C4×C5
HallC5×Dic341 ⋊ C3
HallC5×C11×C31⋊C3 ⋊ C4
HallC5×C11×C31 ⋊ C3×C4
HallDic341 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C4×C5
HallC5×C31⋊C3 ⋊ Dic11
HallC5×C31 ⋊ C3×Dic11
HallC31⋊C3 ⋊ C5×Dic11
HallC5×C11 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ C3×C5×Dic11
SylowC11 ⋊ C5×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊(D31⋊C3)
commutator, hypocenterC11×C31C3×C4×C5
FrattiniC2C5×C11⋊(D31⋊C3)
Fitting, socleC2×C5×C11×C31C2×C3
prime radicalC2×C5×C11×C31⋊C3C2
cosocleC2×C11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6820

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 74);