Finite Group Databasebeta

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C2×C3×C5×D555 #45686517

order33300
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D555
unambiguous semidirect product(C2×C3)⋊(C3×C5×D185)
unambiguous semidirect product(C2×C5)⋊(C3×C5×D111)

Splittings

Fitting, socleC2×C32×C52×C37 ⋊ C2
derivedC3×C5×C37 ⋊ C22×C3×C5
HallC32×C52×C37 ⋊ C22
HallC52×C37 ⋊ C2×C3×D3
HallC32×C37 ⋊ C2×C5×D5
HallC32×C52 ⋊ C2×D37
SylowC37 ⋊ C2×C3×C5×D15
SylowC52 ⋊ C2×C3×D111
SylowC32 ⋊ C2×C5×D185

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D555
commutator, cosocle, hypocenterC3×C5×C37C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C37C2
LCSG ▷ C3×C5×C37
UCSC1 ◁ C2×C3×C5

224 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 2220

Conjugacy classes & character table

8370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 790);