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C5×#14523824⋊C3 #44544346

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

Aliases

direct productC5×#14523824⋊C3
unambiguous semidirect product(C5×#14523824)⋊C3

Splittings

Fitting, socle, HallC5×C13×C41 ⋊ C3×C4
derived, HallC13×C41 ⋊ C3×C4×C5
HallC5×#14523824 ⋊ C3
HallC5×C13⋊C3×C41 ⋊ C4
Hall#14523824 ⋊ C3×C5
HallC13⋊C3×C41 ⋊ C4×C5
HallC5×C41 ⋊ Dic13⋊C3
HallC5×C13⋊C3 ⋊ #4223
HallC5×C13 ⋊ C3×#4223
SylowC41 ⋊ C5×Dic13⋊C3
HallC13⋊C3 ⋊ C5×#4223
SylowC13 ⋊ C3×C5×#4223

Subgroups

subgroupG/H
center, hypercenterC5#14523824⋊C3
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC1G
Fitting, socleC5×C13×C41C3×C4
prime radicalC5×C13⋊C3×D41C2
cosocleC13×D41C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 74);