Finite Group Databasebeta

← Prev (#49114763) Next (#49114765) →

C11×ΓL(1,𝔽8)×C3⋊#261 #49114764

order36036
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)×C3⋊#261
unambiguous semidirect productC3⋊(C11×ΓL(1,𝔽8)×#261)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C3×C4
derivedC3×C7×C13 ⋊ C3×C4×C11
HallC3×C11×C13×ΓL(1,𝔽8) ⋊ C4
HallC7×C11×C13 ⋊ C3×Dic3
HallC3×C13×ΓL(1,𝔽8) ⋊ C4×C11
HallC3×C11×ΓL(1,𝔽8) ⋊ #261
HallC11×C13 ⋊ Dic3×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×C11×Dic3
HallC7×C11 ⋊ C3×C3⋊#261
HallC3×ΓL(1,𝔽8) ⋊ C11×#261
SylowC13 ⋊ C11×Dic3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×C3⋊#261

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×C3⋊#261
commutator, hypocenterC3×C7×C13C3×C4×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C3×C4
prime radicalC3×C11×ΓL(1,𝔽8)×D13C2
cosocleC3×C7×D13C2×C3×C11
LCSG ▷ C3×C7×C13
UCSC1 ◁ C11

112 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 112 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) = 3003

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 432);