Finite Group Databasebeta

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D3×C23×D105 #44394605

order28980
automorphism?
homologyAbelianization (H1) = C22×C23 · Schur multiplier (H2) = C2

Aliases

direct productD3×C23×D105
unambiguous semidirect product(C3×D3)⋊(C23×D35)
unambiguous semidirect product(C5×D3)⋊(C23×D21)
unambiguous semidirect product(D3×C7)⋊(C23×D15)

Splittings

Fitting, socle, HallC32×C5×C7×C23 ⋊ C22
derived, HallC32×C5×C7 ⋊ C22×C23
HallC32×C7×C23 ⋊ C2×D5
HallC32×C5×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ D32
HallC32×C23 ⋊ C2×D35
HallC7×C23 ⋊ D3×D15
HallC5×C23 ⋊ D3×D21
HallC32×C7 ⋊ C2×D5×C23
HallC32×C5 ⋊ C2×D7×C23
HallC5×C7 ⋊ D32×C23
SylowC32 ⋊ C2×C23×D35
SylowC7 ⋊ D3×C23×D15
SylowC5 ⋊ D3×C23×D21

Subgroups

subgroupG/H
center, hypercenterC23D3×D105
commutator, cosocle, hypocenterC32×C5×C7C22×C23
FrattiniC1G
Fitting, socleC32×C5×C7×C23C22
LCSG ▷ C32×C5×C7
UCSC1 ◁ C23

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 4830

Conjugacy classes & character table

3726 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 274);