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C5×C3⋊D483 #28408055

order14490
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C3⋊D483
unambiguous semidirect productC3⋊(C5×D483)
unambiguous semidirect productC7⋊(C5×C3⋊D69)
unambiguous semidirect productC23⋊(C5×C3⋊D21)

Splittings

Fitting, socle, HallC32×C5×C7×C23 ⋊ C2
derived, HallC32×C7×C23 ⋊ C2×C5
HallC32×C5×C23 ⋊ D7
HallC5×C7×C23 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ D23
HallC32×C23 ⋊ C5×D7
HallC7×C23 ⋊ C5×C3⋊D3
HallC5×C23 ⋊ C3⋊D21
HallC32×C7 ⋊ C5×D23
HallC32×C5 ⋊ D161
HallC5×C7 ⋊ C3⋊D69
SylowC23 ⋊ C5×C3⋊D21
SylowC32 ⋊ C5×D161
SylowC7 ⋊ C5×C3⋊D69

Subgroups

subgroupG/H
center, hypercenterC5C3⋊D483
commutator, cosocle, hypocenterC32×C7×C23C2×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C23C2
LCSG ▷ C32×C7×C23
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 7245

A minimal faithful permutation representation — 3 generators on 41 points:

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

Conjugacy classes & character table

3630 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×D483, C5×D21×D69, D15⋊D483, …
maximal normal subgroup ofC5×D3×D483, C5×D21×D69, D15⋊D483, …
maximal quotient ofC5×C3⋊Dic483, C2×C5×C3⋊D483

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 46);