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C3×D2635 #30629030

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

Aliases

direct productC3×D2635
unambiguous semidirect productC5⋊(C3×D527)
unambiguous semidirect productC17⋊(C3×D155)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C2
derived, HallC5×C17×C31 ⋊ C2×C3
HallC3×C17×C31 ⋊ D5
HallC17×C31 ⋊ C3×D5
HallC3×C5×C31 ⋊ D17
HallC3×C5×C17 ⋊ D31
HallC5×C31 ⋊ C3×D17
HallC3×C31 ⋊ D85
HallC5×C17 ⋊ C3×D31
HallC3×C17 ⋊ D155
SylowC31 ⋊ C3×D85
SylowC17 ⋊ C3×D155
HallC3×C5 ⋊ D527
SylowC5 ⋊ C3×D527

Subgroups

subgroupG/H
center, hypercenterC3D2635
commutator, cosocle, hypocenterC5×C17×C31C2×C3
FrattiniC1G
Fitting, socleC3×C5×C17×C31C2
LCSG ▷ C5×C17×C31
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3957 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D31×D85, C3×D17×D155, C3×D5×D527, …
maximal normal subgroup ofC3×D31×D85, C3×D17×D155, C3×D5×D527, …
maximal quotient ofC3×Dic2635, C2×C3×D2635

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 11);