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C31×D255 #30629037

order15810
isoclinismisoclinic class of D255
automorphism?
homologyAbelianization (H1) = C2×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×D255
unambiguous semidirect productC3⋊(C31×D85)
unambiguous semidirect productC5⋊(C31×D51)
unambiguous semidirect productC17⋊(D15×C31)

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C2
derived, HallC3×C5×C17 ⋊ C2×C31
HallC5×C17×C31 ⋊ D3
HallC3×C17×C31 ⋊ D5
HallC17×C31 ⋊ D15
HallC3×C5×C31 ⋊ D17
HallC5×C31 ⋊ D51
HallC3×C31 ⋊ D85
HallC5×C17 ⋊ D3×C31
HallC3×C17 ⋊ D5×C31
SylowC17 ⋊ D15×C31
HallC3×C5 ⋊ C31×D17
SylowC5 ⋊ C31×D51
SylowC3 ⋊ C31×D85

Subgroups

subgroupG/H
center, hypercenterC31D255
commutator, cosocle, hypocenterC3×C5×C17C2×C31
FrattiniC1G
Fitting, socleC3×C5×C17×C31C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3999 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31×D255, D15×C31×D17, D527⋊D15, …
maximal normal subgroup ofD31×D255, D15×C31×D17, D527⋊D15, …
maximal quotient ofC31×Dic255, C2×C31×D255

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 18);