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ΓL(1,𝔽8)×D13×C11⋊C5 #44473333

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×D13×C11⋊C5
unambiguous semidirect product(C11×ΓL(1,𝔽8)×D13)⋊C5

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C2×C3×C5
HallC13×ΓL(1,𝔽8)×C11⋊C5 ⋊ C2
HallC7×D13×C11⋊C5 ⋊ C3
HallC11×ΓL(1,𝔽8)×D13 ⋊ C5
HallC7×C13×C11⋊C5 ⋊ C2×C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C2×C5
HallC7×C11×D13 ⋊ C3×C5
HallC13×C11⋊C5 ⋊ C2×ΓL(1,𝔽8)
HallC7×C11⋊C5 ⋊ C3×D13
HallC11×D13 ⋊ C5×ΓL(1,𝔽8)
HallC13×ΓL(1,𝔽8) ⋊ C2×C11⋊C5
HallC11×ΓL(1,𝔽8) ⋊ C5×D13
HallC7×D13 ⋊ C3×C11⋊C5
HallC11×C13 ⋊ C2×C5×ΓL(1,𝔽8)
HallC7×C13 ⋊ C2×C3×C11⋊C5
HallC7×C11 ⋊ C3×C5×D13
SylowC13 ⋊ C2×ΓL(1,𝔽8)×C11⋊C5
SylowC11 ⋊ C5×ΓL(1,𝔽8)×D13
SylowC7 ⋊ C3×D13×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C13C2×C3×C5
LCSG ▷ C7×C11×C13
UCSC1

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1001

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 118);