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C31×D195 #27130652

order12090
isoclinismisoclinic class of D195
automorphism?
homologyAbelianization (H1) = C2×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×D195
unambiguous semidirect productC3⋊(C31×D65)
unambiguous semidirect productC5⋊(C31×D39)
unambiguous semidirect productC13⋊(D15×C31)

Splittings

Fitting, socle, HallC3×C5×C13×C31 ⋊ C2
derived, HallC3×C5×C13 ⋊ C2×C31
HallC5×C13×C31 ⋊ D3
HallC3×C13×C31 ⋊ D5
HallC3×C5×C31 ⋊ D13
HallC13×C31 ⋊ D15
HallC5×C31 ⋊ D39
HallC3×C31 ⋊ D65
HallC5×C13 ⋊ D3×C31
HallC3×C13 ⋊ D5×C31
HallC3×C5 ⋊ D13×C31
SylowC13 ⋊ D15×C31
SylowC5 ⋊ C31×D39
SylowC3 ⋊ C31×D65

Subgroups

subgroupG/H
center, hypercenterC31D195
commutator, cosocle, hypocenterC3×C5×C13C2×C31
FrattiniC1G
Fitting, socleC3×C5×C13×C31C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3069 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD31×D195, D13×D15×C31, D403⋊D15, …
maximal normal subgroup ofD31×D195, D13×D15×C31, D403⋊D15, …
maximal quotient ofC31×Dic195, C2×C31×D195, C31×D585, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12090, 24);