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C31⋊C3×Dic11⋊C5 #35205666

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

Aliases

direct productC31⋊C3×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C31⋊C3)
unambiguous semidirect product(C11⋊C5)⋊(C4×C31⋊C3)
unambiguous semidirect product(C31×Dic11⋊C5)⋊C3

Splittings

derived, HallC11×C31 ⋊ C3×C4×C5
HallC31×Dic11⋊C5 ⋊ C3
HallC11⋊C5×C31⋊C3 ⋊ C4
HallDic11×C31⋊C3 ⋊ C5
HallC31×C11⋊C5 ⋊ C3×C4
HallC31×Dic11 ⋊ C3×C5
HallC11×C31⋊C3 ⋊ C4×C5
HallC11⋊C5 ⋊ C4×C31⋊C3
HallDic11 ⋊ C5×C31⋊C3
SylowC31 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C4×C5×C31⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C31⋊C3×AGL(1,𝔽11)
commutator, hypocenterC11×C31C3×C4×C5
Fitting, socle, cosocleC2×C11×C31C2×C3×C5
prime radicalC2×C11⋊C5×C31⋊C3C2
LCSG ▷ C11×C31
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1364

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 86);