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C5×Dic1209 #37563722

order24180
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic1209
unambiguous semidirect productC3⋊(C5×Dic403)

Splittings

derived, HallC3×C13×C31 ⋊ C4×C5
HallC3×C5×C13×C31 ⋊ C4
HallC5×C13×C31 ⋊ Dic3
HallC3×C5×C31 ⋊ Dic13
HallC13×C31 ⋊ C5×Dic3
HallC3×C5×C13 ⋊ Dic31
HallC5×C31 ⋊ Dic39
HallC3×C31 ⋊ C5×Dic13
HallC5×C13 ⋊ Dic93
HallC3×C13 ⋊ C5×Dic31
SylowC31 ⋊ C5×Dic39
HallC3×C5 ⋊ Dic403
SylowC13 ⋊ C5×Dic93
SylowC3 ⋊ C5×Dic403

Subgroups

subgroupG/H
center, hypercenterC2×C5D1209
commutator, hypocenterC3×C13×C31C4×C5
FrattiniC2C5×D1209
Fitting, socle, prime radicalC2×C3×C5×C13×C31C2
cosocleC2×C3×C13×C31C2×C5
LCSG ▷ C3×C13×C31
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24180

Conjugacy classes & character table

6060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 21);