Finite Group Databasebeta

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D5×D1173 #37553339

order23460
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD5×D1173
unambiguous semidirect product(C3×D5)⋊D391
unambiguous semidirect product(D5×C17)⋊D69
unambiguous semidirect product(D5×C23)⋊D51

Splittings

Fitting, socle, derived, HallC3×C5×C17×C23 ⋊ C22
HallC5×C17×C23 ⋊ C2×D3
HallC3×C17×C23 ⋊ C2×D5
HallC17×C23 ⋊ D3×D5
HallC3×C5×C23 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D23
HallC5×C23 ⋊ C2×D51
HallC5×C17 ⋊ C2×D69
HallC3×C23 ⋊ D5×D17
HallC3×C17 ⋊ D5×D23
SylowC23 ⋊ D5×D51
SylowC17 ⋊ D5×D69
HallC3×C5 ⋊ C2×D391
SylowC5 ⋊ C2×D1173
SylowC3 ⋊ D5×D391

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C17×C23C22
LCSG ▷ C3×C5×C17×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5865

Conjugacy classes & character table

2352 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 66);