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C13×Dic615 #44544289

order31980
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×Dic615
unambiguous semidirect productC3⋊(C13×Dic205)

Splittings

derived, HallC3×C5×C41 ⋊ C4×C13
HallC3×C5×C13×C41 ⋊ C4
HallC5×C13×C41 ⋊ Dic3
HallC3×C13×C41 ⋊ Dic5
HallC13×C41 ⋊ Dic15
HallC5×C41 ⋊ Dic3×C13
HallC3×C5×C13 ⋊ Dic41
HallC3×C41 ⋊ C13×Dic5
HallC5×C13 ⋊ Dic123
SylowC41 ⋊ C13×Dic15
HallC3×C13 ⋊ Dic205
HallC3×C5 ⋊ C13×Dic41
SylowC5 ⋊ C13×Dic123
SylowC3 ⋊ C13×Dic205

Subgroups

subgroupG/H
center, hypercenterC2×C13D615
commutator, hypocenterC3×C5×C41C4×C13
FrattiniC2C13×D615
Fitting, socle, prime radicalC2×C3×C5×C13×C41C2
cosocleC2×C3×C5×C41C2×C13
LCSG ▷ C3×C5×C41
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31980

Conjugacy classes & character table

8034 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 17);