Finite Group Databasebeta

← Prev (#37528527) Next (#37528529) →

C11×ΓL(1,𝔽8)×#1042 #37528528

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

Aliases

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

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C3×C4
derived, HallC52×C7 ⋊ C3×C4×C11
HallC7×C11×#1042 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C4
HallC7×#1042 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C4×C11
HallC52×C11 ⋊ C4×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×#1042
SylowC52 ⋊ C4×C11×ΓL(1,𝔽8)
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 42 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 42 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 339);