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C3×Dic13×C41⋊C5 #44544293

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic13×C41⋊C5
unambiguous semidirect product(C3×C41×Dic13)⋊C5

Splittings

derived, HallC13×C41 ⋊ C3×C4×C5
HallC3×C13×C41⋊C5 ⋊ C4
HallC3×C41×Dic13 ⋊ C5
HallC13×C41⋊C5 ⋊ C3×C4
HallC41×Dic13 ⋊ C3×C5
HallC3×C13×C41 ⋊ C4×C5
HallC3×C41 ⋊ C5×Dic13
SylowC41 ⋊ C3×C5×Dic13
HallC3×C13 ⋊ C4×C41⋊C5
SylowC13 ⋊ C3×C4×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3D13×C41⋊C5
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC2C3×D13×C41⋊C5
Fitting, socleC2×C3×C13×C41C2×C5
prime radicalC2×C3×C13×C41⋊C5C2
cosocleC2×C13×C41C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6396

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 21);