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ΓL(1,𝔽8)×C5⋊D145 #44478596

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

Aliases

direct productΓL(1,𝔽8)×C5⋊D145
unambiguous semidirect productC5⋊(ΓL(1,𝔽8)×D145)
unambiguous semidirect productC29⋊(ΓL(1,𝔽8)×C5⋊D5)

Splittings

Fitting, socle, derived, HallC52×C7×C29 ⋊ C2×C3
HallC52×ΓL(1,𝔽8)×C29 ⋊ C2
HallC7×C5⋊D145 ⋊ C3
HallC52×C29 ⋊ C2×ΓL(1,𝔽8)
HallΓL(1,𝔽8)×C29 ⋊ C5⋊D5
HallC52×ΓL(1,𝔽8) ⋊ D29
HallC7×C29 ⋊ C3×C5⋊D5
HallC52×C7 ⋊ C3×D29
SylowC29 ⋊ ΓL(1,𝔽8)×C5⋊D5
SylowC52 ⋊ ΓL(1,𝔽8)×D29
SylowC7 ⋊ C3×C5⋊D145

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C29C2×C3
LCSG ▷ C52×C7×C29
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5075

Conjugacy classes & character table

1820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 80);