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C3×C7×C11⋊(ΓL(1,𝔽8)⋊C4) #34084755

order19404
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×C11⋊(ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productC11⋊(C3×C7×ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C7×Dic11)
unambiguous semidirect productDic77⋊(C32×C7)
unambiguous semidirect product(C3×Dic77)⋊(C3×C7)

Splittings

derivedC7×C11 ⋊ C32×C4×C7
HallC3×C7×C11×ΓL(1,𝔽8) ⋊ C4
HallC7×Dic77 ⋊ C32
HallC72×C11 ⋊ C32×C4
HallC3×C7×ΓL(1,𝔽8) ⋊ Dic11
SylowC72 ⋊ C32×Dic11
SylowC11 ⋊ C3×C7×ΓL(1,𝔽8)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C32×C4×C7
FrattiniC2C3×C7×C11⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C72×C11C2×C3
prime radicalC2×C3×C7×C11×ΓL(1,𝔽8)C2
cosocleC2×C7×C11C2×C32×C7
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C7

152 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 2772

Conjugacy classes & character table

1344 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 246);