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#13049959⋊C5 #20266752

order6510
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#13049959⋊C5

Splittings

Fitting, socle, derived, HallC7×C31 ⋊ C2×C3×C5
Hall#10620253⋊C5 ⋊ C2
HallD7×ΓL(1,𝔽32) ⋊ C3
Hall#13049959 ⋊ C5
HallC7×ΓL(1,𝔽32) ⋊ C2×C3
Hall#10620253 ⋊ C2×C5
HallD7×C31 ⋊ C3×C5
HallΓL(1,𝔽32) ⋊ AGL(1,𝔽7)
SylowC31 ⋊ C5×AGL(1,𝔽7)
HallD7 ⋊ (C31⋊C3)⋊C5
SylowC7 ⋊ C2×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C31C2×C3×C5
LCSG ▷ C7×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,5,7,31|d^a=d^6,d^b=d^2,e^b=e^25,e^c=e^16

Conjugacy classes & character table

45 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#13049955⋊C2)⋊C5, C2×#13049959⋊C5, AGL(1,𝔽7)×(C31⋊C3)⋊C5, …
maximal normal subgroup of(#13049955⋊C2)⋊C5, C2×#13049959⋊C5, AGL(1,𝔽7)×(C31⋊C3)⋊C5, …
maximal quotient of#14579600⋊C5, C2×#13049959⋊C5, #16840861⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6510, 67);