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C3×C13×Dic205 #44544281

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×Dic205

Splittings

derived, HallC5×C41 ⋊ C3×C4×C13
HallC3×C5×C13×C41 ⋊ C4
HallC5×C13×C41 ⋊ C3×C4
HallC3×C13×C41 ⋊ Dic5
HallC3×C5×C41 ⋊ C4×C13
HallC13×C41 ⋊ C3×Dic5
HallC3×C5×C13 ⋊ Dic41
HallC3×C41 ⋊ C13×Dic5
HallC5×C13 ⋊ C3×Dic41
SylowC41 ⋊ C3×C13×Dic5
HallC3×C5 ⋊ C13×Dic41
SylowC5 ⋊ C3×C13×Dic41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D205
commutator, hypocenterC5×C41C3×C4×C13
FrattiniC2C3×C13×D205
Fitting, socle, prime radicalC2×C3×C5×C13×C41C2
cosocleC2×C5×C41C2×C3×C13
LCSG ▷ C5×C41
UCSC1 ◁ C2×C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31980

Conjugacy classes & character table

8112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 9);