Finite Group Databasebeta

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C3×C5×D15×C49 #36347704

order22050
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D15×C49
unambiguous semidirect productC3⋊(C3×C5×D5×C49)
unambiguous semidirect productC5⋊(C3×C5×D3×C49)

Splittings

Fitting, HallC32×C52×C49 ⋊ C2
derivedC3×C5 ⋊ C2×C3×C5×C49
HallC52×C49 ⋊ C3×D3
HallC32×C49 ⋊ C5×D5
HallC32×C52 ⋊ C2×C49
SylowC52 ⋊ C3×D3×C49
SylowC32 ⋊ C5×D5×C49

Subgroups

subgroupG/H
center, hypercenterC3×C5×C49D15
commutator, hypocenterC3×C5C2×C3×C5×C49
FrattiniC7C3×C5×C7×D15
FittingC32×C52×C49C2
socleC32×C52×C7C2×C7
prime radicalC3×C5×C7×D15C7
cosocleC3×C5×C7C2×C3×C5×C7
LCSG ▷ C3×C5
UCSC1 ◁ C3×C5×C49

144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1470

Conjugacy classes & character table

6615 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22050, 141);