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C5×D5×ΓL(1,𝔽8)×C29 #44478591

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×D5×ΓL(1,𝔽8)×C29
unambiguous semidirect productC5⋊(C2×C5×ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C7×D5)⋊(C3×C5×C29)
unambiguous semidirect product(C5×C7×D5)⋊(C3×C29)
unambiguous semidirect product(C7×D5×C29)⋊(C3×C5)
unambiguous semidirect product(C5×C7×D5×C29)⋊C3

Splittings

Fitting, socle, HallC52×C7×C29 ⋊ C2×C3
derivedC5×C7 ⋊ C2×C3×C5×C29
HallC52×ΓL(1,𝔽8)×C29 ⋊ C2
HallC5×C7×D5×C29 ⋊ C3
HallC52×C29 ⋊ C2×ΓL(1,𝔽8)
HallC52×ΓL(1,𝔽8) ⋊ C2×C29
HallC5×C7×D5 ⋊ C3×C29
HallC7×C29 ⋊ C3×C5×D5
HallC52×C7 ⋊ C2×C3×C29
SylowC52 ⋊ C2×ΓL(1,𝔽8)×C29
SylowC7 ⋊ C3×C5×D5×C29

Subgroups

subgroupG/H
center, hypercenterC5×C29D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C2×C3×C5×C29
FrattiniC1G
Fitting, socleC52×C7×C29C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C5×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2030

Conjugacy classes & character table

2900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 75);