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C3×Dic2665 #44544283

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

Aliases

direct productC3×Dic2665

Splittings

derived, HallC5×C13×C41 ⋊ C3×C4
HallC3×C5×C13×C41 ⋊ C4
HallC3×C13×C41 ⋊ Dic5
HallC3×C5×C41 ⋊ Dic13
HallC13×C41 ⋊ C3×Dic5
HallC5×C41 ⋊ C3×Dic13
HallC3×C5×C13 ⋊ Dic41
HallC3×C41 ⋊ Dic65
HallC5×C13 ⋊ C3×Dic41
SylowC41 ⋊ C3×Dic65
HallC3×C13 ⋊ Dic205
HallC3×C5 ⋊ Dic533
SylowC13 ⋊ C3×Dic205
SylowC5 ⋊ C3×Dic533

Subgroups

subgroupG/H
center, hypercenterC2×C3D2665
commutator, hypocenterC5×C13×C41C3×C4
FrattiniC2C3×D2665
Fitting, socle, prime radicalC2×C3×C5×C13×C41C2
cosocleC2×C5×C13×C41C2×C3
LCSG ▷ C5×C13×C41
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31980

Conjugacy classes & character table

8004 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 11);