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C11×ΓL(1,𝔽8)×#3866 #46803207

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

Aliases

direct productC11×ΓL(1,𝔽8)×#3866

Splittings

Fitting, socle, HallC7×C11×C37 ⋊ C3×C4
derived, HallC7×C37 ⋊ C3×C4×C11
HallC7×C11×#3866 ⋊ C3
HallC11×ΓL(1,𝔽8)×C37 ⋊ C4
HallC7×#3866 ⋊ C3×C11
HallΓL(1,𝔽8)×C37 ⋊ C4×C11
HallC11×C37 ⋊ C4×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×#3866
SylowC37 ⋊ C4×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×#3866

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×#3866
commutator, hypocenterC7×C37C3×C4×C11
FrattiniC1G
Fitting, socleC7×C11×C37C3×C4
prime radicalC11×ΓL(1,𝔽8)×D37C2
cosocleC7×D37C2×C3×C11
LCSG ▷ C7×C37
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2849

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 79);