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C2×C3⋊((C11⋊C5)⋊D31) #35205802

order20460
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊((C11⋊C5)⋊D31)
unambiguous semidirect product(C2×C3)⋊((C11⋊C5)⋊D31)
unambiguous semidirect product(C2×C11⋊C5)⋊D93

Splittings

Fitting, socleC2×C3×C11×C31 ⋊ C2×C5
derived, HallC3×C11×C31 ⋊ C22×C5
HallC3×C31×C11⋊C5 ⋊ C22
HallC2×D1023 ⋊ C5
HallC31×C11⋊C5 ⋊ C2×D3
HallC11×C31 ⋊ C2×C5×D3
HallC3×C11⋊C5 ⋊ C2×D31
HallC3×C31 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C2×D93
HallC3×C11 ⋊ C2×C5×D31
SylowC31 ⋊ C2×C3⋊AGL(1,𝔽11)
SylowC11 ⋊ C2×C5×D93
SylowC3 ⋊ C2×(C11⋊C5)⋊D31

Subgroups

subgroupG/H
center, hypercenterC2C3⋊((C11⋊C5)⋊D31)
commutator, cosocle, hypocenterC3×C11×C31C22×C5
FrattiniC1G
Fitting, socleC2×C3×C11×C31C2×C5
LCSG ▷ C3×C11×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 2046

A minimal faithful permutation representation — 2 generators on 47 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(33,37,38,36,41,34,35,42,39,40)(44,45);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(32,33,36,41,35,38,42,37,40,39,34)(43,44,45)(46,47)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20460, 222);