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C5×#87705 #14521963

order1995
isoclinismisoclinic class of #87705
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#87705

Splittings

Fitting, socle, HallC5×C7×C19 ⋊ C3
derived, HallC7×C19 ⋊ C3×C5
HallC5×C19 ⋊ ΓL(1,𝔽8)
HallC5×C7 ⋊ C19⋊C3
SylowC19 ⋊ C5×ΓL(1,𝔽8)
SylowC7 ⋊ C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#87705
commutator, cosocle, hypocenterC7×C19C3×C5
FrattiniC1G
Fitting, socleC5×C7×C19C3
LCSG ▷ C7×C19
UCSC1 ◁ C5

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

Conjugacy classes & character table

235 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×#87705, C5×#11716322, C5×#11716326, …
maximal normal subgroup ofC2×C5×#87705, C5×#11716322, C5×#11716326, …
maximal quotient ofC2×C5×#87705, C5×#14584108, C5×C19⋊#3862, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1995, 3);