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#19129741

order5460
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, HallC5×C7×C13 ⋊ C3×C4
HallC7×#63120 ⋊ C3
HallC5×#63270 ⋊ C4
Hall#63270 ⋊ AGL(1,𝔽5)
Hall#63120 ⋊ ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×AGL(1,𝔽5)
HallC5×C13 ⋊ C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ Dic13⋊C3
SylowC13 ⋊ AGL(1,𝔽5)×ΓL(1,𝔽8)
SylowC7 ⋊ #63120⋊C3
SylowC5 ⋊ #11763957

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C13C3×C4
LCSG ▷ C5×C7×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,2,5,7,13|a^2=c,d^a=d^2,f^a=f^12,e^b=e^2,f^b=f^3,d^c=d^4

Conjugacy classes & character table

81 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×#63120⋊C3, C3×#19129741, C3⋊#19129741, …
maximal normal subgroup ofΓL(1,𝔽8)×#63120⋊C3, C3×#19129741, C5×#19129741, …
maximal quotient of#30655033, C3×#19129741, C3⋊#19129741, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 83);