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C3×C13×Dic41⋊C5 #44544292

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×Dic41⋊C5
unambiguous semidirect productDic41⋊(C3×C5×C13)
unambiguous semidirect product(C3×Dic41)⋊(C5×C13)
unambiguous semidirect product(C3×C13×Dic41)⋊C5

Splittings

derived, SylowC41 ⋊ C3×C4×C5×C13
HallC3×C13×C41⋊C5 ⋊ C4
HallC3×C13×Dic41 ⋊ C5
HallC13×C41⋊C5 ⋊ C3×C4
HallC13×Dic41 ⋊ C3×C5
HallC3×C13×C41 ⋊ C4×C5
HallC3×C41⋊C5 ⋊ C4×C13
HallC13×C41 ⋊ C3×C4×C5
HallC3×Dic41 ⋊ C5×C13
HallC41⋊C5 ⋊ C3×C4×C13
HallDic41 ⋊ C3×C5×C13
HallC3×C41 ⋊ C4×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D41⋊C5
commutator, hypocenterC41C3×C4×C5×C13
FrattiniC2C3×C13×D41⋊C5
Fitting, socleC2×C3×C13×C41C2×C5
prime radicalC2×C3×C13×C41⋊C5C2
cosocleC2×C41C2×C3×C5×C13
LCSG ▷ C41
UCSC1 ◁ C2×C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6396

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 20);