Finite Group Databasebeta

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C3×C5×D527 #30629026

order15810
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D527
unambiguous semidirect productC17⋊(C3×C5×D31)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C2
derived, HallC17×C31 ⋊ C2×C3×C5
HallC5×C17×C31 ⋊ C2×C3
HallC3×C17×C31 ⋊ C2×C5
HallC3×C5×C31 ⋊ D17
HallC3×C5×C17 ⋊ D31
HallC5×C31 ⋊ C3×D17
HallC3×C31 ⋊ C5×D17
HallC5×C17 ⋊ C3×D31
HallC3×C17 ⋊ C5×D31
SylowC31 ⋊ C3×C5×D17
SylowC17 ⋊ C3×C5×D31

Subgroups

subgroupG/H
center, hypercenterC3×C5D527
commutator, cosocle, hypocenterC17×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C31C2
LCSG ▷ C17×C31
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3975 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D17×D31, C3×D5×D527, C3×D85⋊D31, …
maximal normal subgroup ofC3×C5×D17×D31, C3×D5×D527, C3×D85⋊D31, …
maximal quotient ofC3×C5×Dic527, C2×C3×C5×D527

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 7);