Finite Group Databasebeta

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C2×C5×C3⋊D555 #45686523

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

Aliases

direct productC2×C5×C3⋊D555
unambiguous semidirect product(C2×C3)⋊(C5×D555)
unambiguous semidirect product(C2×C5)⋊(C5×C3⋊D111)
unambiguous semidirect product(C2×C37)⋊(C5×C3⋊D15)

Splittings

Fitting, socleC2×C32×C52×C37 ⋊ C2
derivedC32×C5×C37 ⋊ C22×C5
HallC32×C52×C37 ⋊ C22
HallC52×C37 ⋊ C2×C3⋊D3
HallC32×C37 ⋊ C2×C5×D5
HallC32×C52 ⋊ C2×D37
SylowC37 ⋊ C2×C5×C3⋊D15
SylowC52 ⋊ C2×C3⋊D111
SylowC32 ⋊ C2×C5×D185

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D555
commutator, cosocle, hypocenterC32×C5×C37C22×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C37C2
LCSG ▷ C32×C5×C37
UCSC1 ◁ C2×C5

288 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 6660

Conjugacy classes & character table

8340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 796);