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C5×D1743 #31775233

order17430
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1743
unambiguous semidirect productC3⋊(C5×D581)
unambiguous semidirect productC7⋊(C5×D249)
unambiguous semidirect productC83⋊(C5×D21)

Splittings

Fitting, socle, HallC3×C5×C7×C83 ⋊ C2
derived, HallC3×C7×C83 ⋊ C2×C5
HallC5×C7×C83 ⋊ D3
HallC3×C5×C83 ⋊ D7
HallC7×C83 ⋊ C5×D3
HallC5×C83 ⋊ D21
HallC3×C83 ⋊ C5×D7
HallC3×C5×C7 ⋊ D83
SylowC83 ⋊ C5×D21
HallC5×C7 ⋊ D249
HallC3×C7 ⋊ C5×D83
HallC3×C5 ⋊ D581
SylowC7 ⋊ C5×D249
SylowC3 ⋊ C5×D581

Subgroups

subgroupG/H
center, hypercenterC5D1743
commutator, cosocle, hypocenterC3×C7×C83C2×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C83C2
LCSG ▷ C3×C7×C83
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8715

Conjugacy classes & character table

4365 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D21×D83, C5×D7×D249, C5×D3×D581, …
maximal normal subgroup ofC5×D21×D83, C5×D7×D249, C5×D3×D581, …
maximal quotient ofC5×Dic1743, C2×C5×D1743

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17430, 13);