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C5×C13×Dic129 #46776394

order33540
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×Dic129
unambiguous semidirect productC3⋊(C5×C13×Dic43)
unambiguous semidirect productC43⋊(C5×Dic3×C13)

Splittings

derived, HallC3×C43 ⋊ C4×C5×C13
HallC3×C5×C13×C43 ⋊ C4
HallC5×C13×C43 ⋊ Dic3
HallC3×C13×C43 ⋊ C4×C5
HallC3×C5×C43 ⋊ C4×C13
HallC13×C43 ⋊ C5×Dic3
HallC5×C43 ⋊ Dic3×C13
HallC3×C5×C13 ⋊ Dic43
SylowC43 ⋊ C5×Dic3×C13
HallC3×C13 ⋊ C5×Dic43
HallC3×C5 ⋊ C13×Dic43
SylowC3 ⋊ C5×C13×Dic43

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D129
commutator, hypocenterC3×C43C4×C5×C13
FrattiniC2C5×C13×D129
Fitting, socle, prime radicalC2×C3×C5×C13×C43C2
cosocleC2×C3×C43C2×C5×C13
LCSG ▷ C3×C43
UCSC1 ◁ C2×C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33540

Conjugacy classes & character table

8580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 14);