Finite Group Databasebeta

← Prev (#44394529) Next (#44394531) →

C2×C5×D3×ΓL(1,𝔽8)×C23 #44394530

order28980
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D3×ΓL(1,𝔽8)×C23
unambiguous semidirect productC3⋊(C22×C5×ΓL(1,𝔽8)×C23)
unambiguous semidirect product(C2×C3)⋊(C2×C5×ΓL(1,𝔽8)×C23)
unambiguous semidirect product(C2×D3×C7)⋊(C3×C5×C23)
unambiguous semidirect product(C2×C5×D3×C7)⋊(C3×C23)
unambiguous semidirect product(C2×D3×C7×C23)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D3×C7×C23)⋊C3

Splittings

Fitting, socleC2×C3×C5×C7×C23 ⋊ C2×C3
derivedC3×C7 ⋊ C22×C3×C5×C23
HallC3×C5×ΓL(1,𝔽8)×C23 ⋊ C22
HallC3×ΓL(1,𝔽8)×C23 ⋊ C22×C5
HallC5×C7×C23 ⋊ C2×C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ C22×C23
HallC7×C23 ⋊ C2×C3×C5×D3
HallC3×ΓL(1,𝔽8) ⋊ C22×C5×C23
HallC5×C7 ⋊ C2×C3×D3×C23
SylowC7 ⋊ C2×C3×C5×D3×C23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C23D3×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC3×C7C22×C3×C5×C23
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C23C2×C3
LCSG ▷ C3×C7
UCSC1 ◁ C2×C5×C23

176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 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

3450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 199);