Finite Group Databasebeta

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C11×Dic3×#63270 #49114577

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

Aliases

direct productC11×Dic3×#63270
unambiguous semidirect productC3⋊(C4×C11×#63270)

Splittings

derivedC3×C7×C13 ⋊ C3×C4×C11
HallC3×C11×#63270 ⋊ C4
HallC7×C11×C13 ⋊ C3×Dic3
HallC3×#63270 ⋊ C4×C11
HallC11×C13 ⋊ Dic3×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×C11×Dic3
HallC7×C11 ⋊ Dic3×C13⋊C3
SylowC13 ⋊ C11×Dic3×ΓL(1,𝔽8)
SylowC7 ⋊ C11×Dic3×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11D3×#63270
commutator, hypocenterC3×C7×C13C3×C4×C11
FrattiniC2D3×C11×#63270
Fitting, socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×C11×#63270C2
cosocleC2×C3×C7×C13C2×C3×C11
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C11

112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 12012

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 245);