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C11×C3⋊(C5⋊D95) #44535541

order31350
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×C3⋊(C5⋊D95)
unambiguous semidirect productC3⋊(C11×C5⋊D95)
unambiguous semidirect productC5⋊(C11×D285)
unambiguous semidirect productC19⋊(C11×C3⋊(C5⋊D5))

Splittings

Fitting, socle, HallC3×C52×C11×C19 ⋊ C2
derived, HallC3×C52×C19 ⋊ C2×C11
HallC52×C11×C19 ⋊ D3
HallC3×C52×C11 ⋊ D19
HallC3×C11×C19 ⋊ C5⋊D5
HallC52×C19 ⋊ D3×C11
HallC52×C11 ⋊ D57
HallC11×C19 ⋊ C3⋊(C5⋊D5)
HallC3×C52 ⋊ C11×D19
HallC3×C19 ⋊ C11×C5⋊D5
HallC3×C11 ⋊ C5⋊D95
SylowC52 ⋊ C11×D57
SylowC19 ⋊ C11×C3⋊(C5⋊D5)
SylowC3 ⋊ C11×C5⋊D95

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C5⋊D95)
commutator, cosocle, hypocenterC3×C52×C19C2×C11
FrattiniC1G
Fitting, socleC3×C52×C11×C19C2
LCSG ▷ C3×C52×C19
UCSC1 ◁ C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 15675

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

7854 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 114);