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C5×C7×C19×AGL(1,𝔽5) #27210884

order13300
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C19 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C19×AGL(1,𝔽5)

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C4
derivedC5 ⋊ C4×C5×C7×C19
HallC52×C19 ⋊ C4×C7
HallC52×C7 ⋊ C4×C19
SylowC52 ⋊ C4×C7×C19

Subgroups

subgroupG/H
center, hypercenterC5×C7×C19AGL(1,𝔽5)
commutator, hypocenterC5C4×C5×C7×C19
FrattiniC1G
Fitting, socleC52×C7×C19C4
prime radicalC5×C7×D5×C19C2
cosocleD5C2×C5×C7×C19
LCSG ▷ C5
UCSC1 ◁ C5×C7×C19

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 2660

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4,5)(7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32,33,34,35,36);(6,7,8,10,9)

Conjugacy classes & character table

3325 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 42);