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ΓL(1,𝔽8)×C3⋊(Dic11⋊C5) #28357478

order13860
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C3⋊(Dic11⋊C5)
unambiguous semidirect productC3⋊(ΓL(1,𝔽8)×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(Dic3×ΓL(1,𝔽8))
unambiguous semidirect productDic33⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(ΓL(1,𝔽8)×Dic33)⋊C5
unambiguous semidirect product(C7×C3⋊(Dic11⋊C5))⋊C3

Splittings

derivedC3×C7×C11 ⋊ C3×C4×C5
HallC3×ΓL(1,𝔽8)×C11⋊C5 ⋊ C4
HallΓL(1,𝔽8)×Dic33 ⋊ C5
HallC3×C11×ΓL(1,𝔽8) ⋊ C4×C5
HallC7×C11⋊C5 ⋊ C3×Dic3
HallC7×C11 ⋊ C3×C5×Dic3
HallC3×ΓL(1,𝔽8) ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ Dic3×ΓL(1,𝔽8)
SylowC11 ⋊ C5×Dic3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C3⋊(Dic11⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C7×C11C3×C4×C5
Fitting, socle, cosocleC2×C3×C7×C11C2×C3×C5
prime radicalC2×C3×ΓL(1,𝔽8)×C11⋊C5C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2

112 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 42 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) = 924

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 145);