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C2×C5×C3⋊D345 #35208253

order20700
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C3⋊D345
unambiguous semidirect product(C2×C3)⋊(C5×D345)
unambiguous semidirect product(C2×C5)⋊(C5×C3⋊D69)
unambiguous semidirect product(C2×C23)⋊(C5×C3⋊D15)

Splittings

Fitting, socleC2×C32×C52×C23 ⋊ C2
derivedC32×C5×C23 ⋊ C22×C5
HallC32×C52×C23 ⋊ C22
HallC52×C23 ⋊ C2×C3⋊D3
HallC32×C52 ⋊ C2×D23
HallC32×C23 ⋊ C2×C5×D5
SylowC52 ⋊ C2×C3⋊D69
SylowC23 ⋊ C2×C5×C3⋊D15
SylowC32 ⋊ C2×C5×D115

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D345
commutator, cosocle, hypocenterC32×C5×C23C22×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C23C2
LCSG ▷ C32×C5×C23
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) = 4140

Conjugacy classes & character table

5190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 369);