Finite Group Databasebeta

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C3×C7×C13×Dic33 #49114607

order36036
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C13×Dic33
unambiguous semidirect productC3⋊(C3×C7×C13×Dic11)
unambiguous semidirect productC11⋊(C3×C7×Dic3×C13)

Splittings

derivedC3×C11 ⋊ C3×C4×C7×C13
HallC32×C7×C11×C13 ⋊ C4
HallC32×C11×C13 ⋊ C4×C7
HallC7×C11×C13 ⋊ C3×Dic3
HallC32×C7×C13 ⋊ Dic11
HallC32×C7×C11 ⋊ C4×C13
HallC11×C13 ⋊ C3×C7×Dic3
HallC32×C13 ⋊ C7×Dic11
HallC32×C11 ⋊ C4×C7×C13
HallC7×C11 ⋊ C3×Dic3×C13
HallC32×C7 ⋊ C13×Dic11
SylowC11 ⋊ C3×C7×Dic3×C13
SylowC32 ⋊ C7×C13×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C13D33
commutator, hypocenterC3×C11C3×C4×C7×C13
FrattiniC2C3×C7×C13×D33
Fitting, socle, prime radicalC2×C32×C7×C11×C13C2
cosocleC2×C3×C11C2×C3×C7×C13
LCSG ▷ C3×C11
UCSC1 ◁ C2×C3×C7×C13

112 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 72 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

9828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 275);