Finite Group Databasebeta

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C2×C3×C5×C7×D69 #44394670

order28980
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C7×D69
unambiguous semidirect product(C2×C3)⋊(C3×C5×C7×D23)
unambiguous semidirect product(C2×C23)⋊(C3×C5×D3×C7)

Splittings

Fitting, socleC2×C32×C5×C7×C23 ⋊ C2
derivedC3×C23 ⋊ C22×C3×C5×C7
HallC32×C5×C7×C23 ⋊ C22
HallC32×C7×C23 ⋊ C22×C5
HallC32×C5×C23 ⋊ C22×C7
HallC5×C7×C23 ⋊ C2×C3×D3
HallC32×C5×C7 ⋊ C2×D23
HallC32×C23 ⋊ C22×C5×C7
HallC7×C23 ⋊ C2×C3×C5×D3
HallC5×C23 ⋊ C2×C3×D3×C7
HallC32×C7 ⋊ C2×C5×D23
HallC32×C5 ⋊ C2×C7×D23
SylowC23 ⋊ C2×C3×C5×D3×C7
SylowC32 ⋊ C2×C5×C7×D23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D69
commutator, cosocle, hypocenterC3×C23C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C23C2
LCSG ▷ C3×C23
UCSC1 ◁ C2×C3×C5×C7

176 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 9660

Conjugacy classes & character table

7560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 339);