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C11×C37×ΓL(1,𝔽8)⋊C4 #46803162

order34188
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C37 · Schur multiplier (H2) = C1

Aliases

direct productC11×C37×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C11×C37)
unambiguous semidirect productDic7⋊(C3×C11×C37)
unambiguous semidirect product(C11×Dic7)⋊(C3×C37)

Splittings

derived, SylowC7 ⋊ C3×C4×C11×C37
HallC11×Dic7×C37 ⋊ C3
HallC11×ΓL(1,𝔽8)×C37 ⋊ C4
HallC7×C11×C37 ⋊ C3×C4
HallDic7×C37 ⋊ C3×C11
HallΓL(1,𝔽8)×C37 ⋊ C4×C11
HallC11×Dic7 ⋊ C3×C37
HallC7×C37 ⋊ C3×C4×C11
HallC11×ΓL(1,𝔽8) ⋊ C4×C37
HallC7×C11 ⋊ C3×C4×C37
HallDic7 ⋊ C3×C11×C37
HallΓL(1,𝔽8) ⋊ C4×C11×C37

Subgroups

subgroupG/H
center, hypercenterC2×C11×C37AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C11×C37
FrattiniC2C11×C37×AGL(1,𝔽7)
Fitting, socleC2×C7×C11×C37C2×C3
prime radicalC2×C11×ΓL(1,𝔽8)×C37C2
cosocleC2×C7C2×C3×C11×C37
LCSG ▷ C7
UCSC1 ◁ C2×C11×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11396

Conjugacy classes & character table

5698 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 34);