Finite Group Databasebeta

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C2×C3×C3⋊(C5⋊D185) #45686519

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C5⋊D185)
commutator, cosocle, hypocenterC3×C52×C37C22×C3
FrattiniC1G
Fitting, socleC2×C32×C52×C37C2
LCSG ▷ C3×C52×C37
UCSC1 ◁ C2×C3

352 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 11100

Conjugacy classes & character table

8334 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 792);