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C11×ΓL(1,𝔽8)⋊Dic37 #46803166

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

Aliases

direct productC11×ΓL(1,𝔽8)⋊Dic37
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×Dic37)

Splittings

derived, HallC7×C37 ⋊ C3×C4×C11
HallC11×Dic259 ⋊ C3
HallC11×ΓL(1,𝔽8)×C37 ⋊ C4
HallC7×C11×C37 ⋊ C3×C4
HallDic259 ⋊ C3×C11
HallΓL(1,𝔽8)×C37 ⋊ C4×C11
HallC11×C37 ⋊ ΓL(1,𝔽8)⋊C4
HallC11×ΓL(1,𝔽8) ⋊ Dic37
HallC7×C11 ⋊ C3×Dic37
SylowC37 ⋊ C11×ΓL(1,𝔽8)⋊C4
HallΓL(1,𝔽8) ⋊ C11×Dic37
SylowC7 ⋊ C3×C11×Dic37

Subgroups

subgroupG/H
center, hypercenterC2×C11ΓL(1,𝔽8)⋊D37
commutator, hypocenterC7×C37C3×C4×C11
FrattiniC2C11×ΓL(1,𝔽8)⋊D37
Fitting, socleC2×C7×C11×C37C2×C3
prime radicalC2×C11×ΓL(1,𝔽8)×C37C2
cosocleC2×C7×C37C2×C3×C11
LCSG ▷ C7×C37
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11396

Conjugacy classes & character table

2134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 38);