Finite Group Databasebeta

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D5×D1677 #46776582

order33540
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD5×D1677
unambiguous semidirect product(C3×D5)⋊D559
unambiguous semidirect product(D5×C13)⋊D129
unambiguous semidirect product(D5×C43)⋊D39

Splittings

Fitting, socle, derived, HallC3×C5×C13×C43 ⋊ C22
HallC5×C13×C43 ⋊ C2×D3
HallC3×C13×C43 ⋊ C2×D5
HallC3×C5×C43 ⋊ C2×D13
HallC13×C43 ⋊ D3×D5
HallC5×C43 ⋊ C2×D39
HallC3×C5×C13 ⋊ C2×D43
HallC3×C43 ⋊ D5×D13
HallC5×C13 ⋊ C2×D129
SylowC43 ⋊ D5×D39
HallC3×C13 ⋊ D5×D43
HallC3×C5 ⋊ C2×D559
SylowC13 ⋊ D5×D129
SylowC5 ⋊ C2×D1677
SylowC3 ⋊ D5×D559

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C13×C43C22
LCSG ▷ C3×C5×C13×C43
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

3360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 202);