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C11×ΓL(1,𝔽8)⋊#1042 #37528526

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊#1042
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×#1042)
unambiguous semidirect product(C7⋊#1042)⋊(C3×C11)
unambiguous semidirect product(C11×C7⋊#1042)⋊C3

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C3×C4
derived, HallC52×C7 ⋊ C3×C4×C11
HallC11×C7⋊#1042 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C4
HallC7⋊#1042 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C4×C11
HallC52×C11 ⋊ ΓL(1,𝔽8)⋊C4
HallC11×ΓL(1,𝔽8) ⋊ #1042
HallC7×C11 ⋊ C3×#1042
SylowC52 ⋊ C11×ΓL(1,𝔽8)⋊C4
HallΓL(1,𝔽8) ⋊ C11×#1042
SylowC7 ⋊ C3×C11×#1042

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)⋊#1042
commutator, hypocenterC52×C7C3×C4×C11
FrattiniC1G
Fitting, socleC52×C7×C11C3×C4
prime radicalC5×D5×C11×ΓL(1,𝔽8)C2
cosocleC5×C7×D5C2×C3×C11
LCSG ▷ C52×C7
UCSC1 ◁ C11

104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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) = 1540

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 337);