Finite Group Databasebeta

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C3×C5×D581 #31775225

order17430
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D581
unambiguous semidirect productC83⋊(C3×C5×D7)

Splittings

Fitting, socle, HallC3×C5×C7×C83 ⋊ C2
derived, HallC7×C83 ⋊ C2×C3×C5
HallC5×C7×C83 ⋊ C2×C3
HallC3×C7×C83 ⋊ C2×C5
HallC3×C5×C83 ⋊ D7
HallC5×C83 ⋊ C3×D7
HallC3×C83 ⋊ C5×D7
HallC3×C5×C7 ⋊ D83
SylowC83 ⋊ C3×C5×D7
HallC5×C7 ⋊ C3×D83
HallC3×C7 ⋊ C5×D83
SylowC7 ⋊ C3×C5×D83

Subgroups

subgroupG/H
center, hypercenterC3×C5D581
commutator, cosocle, hypocenterC7×C83C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C83C2
LCSG ▷ C7×C83
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8715

Conjugacy classes & character table

4380 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D7×D83, C3×D5×D581, C3×D35⋊D83, …
maximal normal subgroup ofC3×C5×D7×D83, C3×D5×D581, C3×D35⋊D83, …
maximal quotient ofC3×C5×Dic581, C2×C3×C5×D581

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17430, 5);