Finite Group Databasebeta

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C3×Dic3003 #49114602

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

Aliases

direct productC3×Dic3003
unambiguous semidirect productC3⋊(C3×Dic1001)
unambiguous semidirect productC11⋊(C3×Dic273)

Splittings

derivedC3×C7×C11×C13 ⋊ C3×C4
HallC32×C7×C11×C13 ⋊ C4
HallC32×C11×C13 ⋊ Dic7
HallC7×C11×C13 ⋊ C3×Dic3
HallC32×C7×C13 ⋊ Dic11
HallC32×C7×C11 ⋊ Dic13
HallC11×C13 ⋊ C3×Dic21
HallC32×C13 ⋊ Dic77
HallC32×C11 ⋊ Dic91
HallC7×C13 ⋊ C3×Dic33
HallC7×C11 ⋊ C3×Dic39
HallC32×C7 ⋊ Dic143
SylowC13 ⋊ C3×Dic231
SylowC11 ⋊ C3×Dic273
SylowC32 ⋊ Dic1001
SylowC7 ⋊ C3×Dic429

Subgroups

subgroupG/H
center, hypercenterC2×C3D3003
commutator, hypocenterC3×C7×C11×C13C3×C4
FrattiniC2C3×D3003
Fitting, socle, prime radicalC2×C32×C7×C11×C13C2
cosocleC2×C3×C7×C11×C13C2×C3
LCSG ▷ C3×C7×C11×C13
UCSC1 ◁ C2×C3

112 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 66 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

9018 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 270);