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D5×#87704 #16860652

order3990
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productD5×#87704
unambiguous semidirect productC5⋊(C2×#87704)

Splittings

Fitting, socle, derived, HallC5×C7×C19 ⋊ C2×C3
HallC5×#87704 ⋊ C2
HallC7×D5×C19 ⋊ C3
HallD5×C19 ⋊ ΓL(1,𝔽8)
HallC7×C19 ⋊ C3×D5
HallC5×C19 ⋊ C2×ΓL(1,𝔽8)
HallC7×D5 ⋊ C19⋊C3
HallC5×C7 ⋊ C2×C19⋊C3
SylowC19 ⋊ D5×ΓL(1,𝔽8)
SylowC7 ⋊ D5×C19⋊C3
SylowC5 ⋊ C2×#87704

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 665

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2,3,4,5)(7,8,10)(9,12,13)(11,15,14)(16,20,18)(17,21,19)(22,24,23)(26,27,28)(29,31,30);(2,5)(3,4)(6,7,9,13,18,23,20,8,11,16,21,10,14,19,12,17,22,24,15)(25,26,27,29,28,30,31)

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×ΓL(1,𝔽8)×C19⋊C3, C3×D5×#87704, D15×#87704, …
maximal normal subgroup ofD5×ΓL(1,𝔽8)×C19⋊C3, C3×D5×#87704, C5×D5×#87704, …
maximal quotient ofD5×#11924776, C3×D5×#87704, D15×#87704, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3990, 35);