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C2×C13×ΓL(1,𝔽8)×C11⋊C5 #44473223

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC2×C13×ΓL(1,𝔽8)×C11⋊C5
unambiguous semidirect product(C2×C7)⋊(C3×C13×C11⋊C5)
unambiguous semidirect product(C2×C11)⋊(C5×C13×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C11×ΓL(1,𝔽8))⋊(C5×C13)
unambiguous semidirect product(C2×C7×C11⋊C5)⋊(C3×C13)
unambiguous semidirect product(C2×C11×C13×ΓL(1,𝔽8))⋊C5

Splittings

Fitting, socle, HallC2×C7×C11×C13 ⋊ C3×C5
derived, HallC7×C11 ⋊ C2×C3×C5×C13
HallC2×C7×C13×C11⋊C5 ⋊ C3
HallC2×C11×C13×ΓL(1,𝔽8) ⋊ C5
HallC7×C13×C11⋊C5 ⋊ C2×C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C2×C5
HallC7×C11×C13 ⋊ C2×C3×C5
HallC2×C7×C11⋊C5 ⋊ C3×C13
HallC2×C11×ΓL(1,𝔽8) ⋊ C5×C13
HallC7×C11⋊C5 ⋊ C2×C3×C13
HallC2×C11×C13 ⋊ C5×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ C2×C5×C13
HallC2×C7×C13 ⋊ C3×C11⋊C5
HallC2×C7×C11 ⋊ C3×C5×C13
HallC11×C13 ⋊ C2×C5×ΓL(1,𝔽8)
HallC7×C13 ⋊ C2×C3×C11⋊C5
HallC2×C11 ⋊ C5×C13×ΓL(1,𝔽8)
HallC2×C7 ⋊ C3×C13×C11⋊C5
SylowC11 ⋊ C2×C5×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C3×C13×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C13ΓL(1,𝔽8)×C11⋊C5
commutator, cosocle, hypocenterC7×C11C2×C3×C5×C13
FrattiniC1G
Fitting, socleC2×C7×C11×C13C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2002

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 8);