Finite Group Databasebeta

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C3×C7×C13×Dic15 #30655271

order16380
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C13×Dic15
unambiguous semidirect productC3⋊(C3×C7×C13×Dic5)

Splittings

derivedC3×C5 ⋊ C3×C4×C7×C13
HallC32×C5×C7×C13 ⋊ C4
HallC32×C7×C13 ⋊ Dic5
HallC32×C5×C13 ⋊ C4×C7
HallC5×C7×C13 ⋊ C3×Dic3
HallC32×C5×C7 ⋊ C4×C13
HallC32×C13 ⋊ C7×Dic5
HallC5×C13 ⋊ C3×C7×Dic3
HallC32×C7 ⋊ C13×Dic5
HallC32×C5 ⋊ C4×C7×C13
HallC5×C7 ⋊ C3×Dic3×C13
SylowC32 ⋊ C7×C13×Dic5
SylowC5 ⋊ C3×C7×Dic3×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C13D15
commutator, hypocenterC3×C5C3×C4×C7×C13
FrattiniC2C3×C7×C13×D15
Fitting, socle, prime radicalC2×C32×C5×C7×C13C2
cosocleC2×C3×C5C2×C3×C7×C13
LCSG ▷ C3×C5
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) = 5460

Conjugacy classes & character table

4914 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 321);