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ΓL(1,𝔽8)×C37×Dic11 #46803154

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

Aliases

direct productΓL(1,𝔽8)×C37×Dic11
unambiguous semidirect productC11⋊(C4×ΓL(1,𝔽8)×C37)
unambiguous semidirect product(C7×Dic11)⋊(C3×C37)

Splittings

derived, HallC7×C11 ⋊ C3×C4×C37
HallC7×C37×Dic11 ⋊ C3
HallC11×ΓL(1,𝔽8)×C37 ⋊ C4
HallC7×C11×C37 ⋊ C3×C4
HallC11×C37 ⋊ C4×ΓL(1,𝔽8)
HallC7×Dic11 ⋊ C3×C37
HallC7×C37 ⋊ C3×Dic11
HallC11×ΓL(1,𝔽8) ⋊ C4×C37
SylowC11 ⋊ C4×ΓL(1,𝔽8)×C37
SylowC7 ⋊ C3×C37×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C37ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C3×C4×C37
FrattiniC2ΓL(1,𝔽8)×D11×C37
Fitting, socleC2×C7×C11×C37C2×C3
prime radicalC2×C11×ΓL(1,𝔽8)×C37C2
cosocleC2×C7×C11C2×C3×C37
LCSG ▷ C7×C11
UCSC1 ◁ C2×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11396

Conjugacy classes & character table

2590 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 26);