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C73×ΓL(1,𝔽8)⋊AGL(1,𝔽5) #44501303

order30660
automorphism?
homologyAbelianization (H1) = C3×C4×C73 · Schur multiplier (H2) = C1

Aliases

direct productC73×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
unambiguous semidirect productΓL(1,𝔽8)⋊(AGL(1,𝔽5)×C73)
unambiguous semidirect product(C7⋊AGL(1,𝔽5))⋊(C3×C73)

Splittings

Fitting, socle, HallC5×C7×C73 ⋊ C3×C4
derived, HallC5×C7 ⋊ C3×C4×C73
HallC73×C7⋊AGL(1,𝔽5) ⋊ C3
HallC5×ΓL(1,𝔽8)×C73 ⋊ C4
HallΓL(1,𝔽8)×C73 ⋊ AGL(1,𝔽5)
HallC7×C73 ⋊ C3×AGL(1,𝔽5)
HallC5×C73 ⋊ ΓL(1,𝔽8)⋊C4
HallC7⋊AGL(1,𝔽5) ⋊ C3×C73
HallC5×ΓL(1,𝔽8) ⋊ C4×C73
HallΓL(1,𝔽8) ⋊ AGL(1,𝔽5)×C73
SylowC7 ⋊ C3×AGL(1,𝔽5)×C73
SylowC5 ⋊ C73×ΓL(1,𝔽8)⋊C4

Subgroups

subgroupG/H
center, hypercenterC73ΓL(1,𝔽8)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C3×C4×C73
FrattiniC1G
Fitting, socleC5×C7×C73C3×C4
prime radicalD5×ΓL(1,𝔽8)×C73C2
cosocleC7×D5C2×C3×C73
LCSG ▷ C5×C7
UCSC1 ◁ C73

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2555

Conjugacy classes & character table

1387 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 66);