Finite Group Databasebeta

← Prev (#46831548) Next (#46831550) →

ΓL(1,𝔽8)×D15×C11⋊C5 #46831549

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D15×C11⋊C5
unambiguous semidirect productC3⋊(D5×ΓL(1,𝔽8)×C11⋊C5)
unambiguous semidirect productC5⋊(D3×ΓL(1,𝔽8)×C11⋊C5)
unambiguous semidirect product(C7×D15)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×D15)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C11×ΓL(1,𝔽8)×D15)⋊C5
unambiguous semidirect product(C7×D15×C11⋊C5)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C7×C11 ⋊ C2×C3×C5
HallC3×C5×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC5×C7×C11⋊C5 ⋊ C3×D3
HallC3×C11×ΓL(1,𝔽8) ⋊ C5×D5
HallC5×C11⋊C5 ⋊ D3×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×C5×D15
HallC3×ΓL(1,𝔽8) ⋊ D5×C11⋊C5
SylowC11 ⋊ C5×ΓL(1,𝔽8)×D15
SylowC7 ⋊ C3×D15×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C11C2×C3×C5
LCSG ▷ C3×C5×C7×C11
UCSC1

192 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 45 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) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 192);