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#27189153

order13020
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, HallC5×C7×C31 ⋊ C3×C4
HallC7×C31⋊AGL(1,𝔽5) ⋊ C3
HallC5×#10620253 ⋊ C4
Hall#10620253 ⋊ AGL(1,𝔽5)
HallC31⋊AGL(1,𝔽5) ⋊ ΓL(1,𝔽8)
HallC7×C31 ⋊ C3×AGL(1,𝔽5)
HallC5×C31 ⋊ C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ AGL(1,𝔽5)×ΓL(1,𝔽8)
SylowC7 ⋊ (C31⋊C3)⋊AGL(1,𝔽5)
SylowC5 ⋊ #14579596

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C31C3×C4
prime radicalD5×#10620253C2
cosocleC7×D5×C31C2×C3
LCSG ▷ C5×C7×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 1085

A minimal faithful permutation representation — 2 generators on 43 points:

(2,6,7,3,4,8)(5,14,15,9,10,22)(11,24,25,17,18,30)(12,23,19,20,16,13)(21,31,28,27,26,29)(33,34,35)(36,38,37)(40,41,42,43);(1,2,5,11,19,7,6,12,21,28,15,23,14,18,26,25,30,31,24,10,16,22,29,27,20,4,8,13,17,9,3)(32,33,34,36,35,37,38)(39,40,41,43,42)

Polycyclic presentation:

2,3,2,5,7,31|a^2=c,d^a=d^2,f^a=f^30,e^b=e^2,f^b=f^25,d^c=d^4

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13020, 120);