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ΓL(1,𝔽8)×C29×C5⋊D5 #44478595

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

Aliases

direct productΓL(1,𝔽8)×C29×C5⋊D5
unambiguous semidirect productC5⋊(D5×ΓL(1,𝔽8)×C29)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC29ΓL(1,𝔽8)×C5⋊D5
commutator, cosocle, hypocenterC52×C7C2×C3×C29
FrattiniC1G
Fitting, socleC52×C7×C29C2×C3
LCSG ▷ C52×C7
UCSC1 ◁ C29

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5075

Conjugacy classes & character table

2030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 79);