Finite Group Databasebeta

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D5×#13110305 #30658752

order16590
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productD5×#13110305
unambiguous semidirect productC5⋊(C2×#13110305)

Splittings

Fitting, socle, derived, HallC5×C7×C79 ⋊ C2×C3
HallC5×#13110305 ⋊ C2
HallC7×D5×C79 ⋊ C3
HallD5×C79 ⋊ ΓL(1,𝔽8)
HallC7×C79 ⋊ C3×D5
HallC5×C79 ⋊ C2×ΓL(1,𝔽8)
SylowC79 ⋊ D5×ΓL(1,𝔽8)
HallC7×D5 ⋊ C79⋊C3
HallC5×C7 ⋊ C2×C79⋊C3
SylowC7 ⋊ D5×C79⋊C3
SylowC5 ⋊ C2×#13110305

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C79C2×C3
LCSG ▷ C5×C7×C79
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2765

Conjugacy classes & character table

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

Relationships

maximal subgroup of#45684426, #45684428, #45684432, …
maximal normal subgroup of#45684426, #45684428, #45684432, …
maximal quotient ofDic5×#13110305, C2×D5×#13110305

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16590, 35);