Finite Group Databasebeta

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C2×C3×C23×C5⋊AGL(1,𝔽7) #44394524

order28980
automorphism?
homologyAbelianization (H1) = C22×C32×C23 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×C23×C5⋊AGL(1,𝔽7)
unambiguous semidirect product(C2×C5)⋊(C3×C23×AGL(1,𝔽7))
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C3×D5×C23)
unambiguous semidirect product(C2×D35)⋊(C32×C23)
unambiguous semidirect product(C2×C3×D35)⋊(C3×C23)
unambiguous semidirect product(C2×C23×D35)⋊C32
unambiguous semidirect product(C2×C3×C23×D35)⋊C3

Splittings

Fitting, socleC2×C3×C5×C7×C23 ⋊ C2×C3
derived, HallC5×C7 ⋊ C22×C32×C23
HallC3×C5×ΓL(1,𝔽8)×C23 ⋊ C22
HallC2×C23×D35 ⋊ C32
HallC3×ΓL(1,𝔽8)×C23 ⋊ C2×D5
HallC5×C7×C23 ⋊ C22×C32
HallC3×C5×ΓL(1,𝔽8) ⋊ C22×C23
HallC7×C23 ⋊ C2×C32×D5
HallC2×D35 ⋊ C32×C23
HallC5×C23 ⋊ C2×C3×AGL(1,𝔽7)
HallC3×ΓL(1,𝔽8) ⋊ C2×D5×C23
SylowC7 ⋊ C2×C32×D5×C23
SylowC5 ⋊ C2×C3×C23×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23C5⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C22×C32×C23
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C23C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C23

240 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 100 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

2346 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 193);