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(ΓL(1,𝔽8)⋊D13)⋊D23 #38737356

order25116
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(ΓL(1,𝔽8)⋊D13)⋊D23
unambiguous semidirect product(ΓL(1,𝔽8)⋊D23)⋊D13

Splittings

Fitting, socle, derived, HallC7×C13×C23 ⋊ C22×C3
HallD91⋊D23 ⋊ C3
HallC13×ΓL(1,𝔽8)×C23 ⋊ C22
HallΓL(1,𝔽8)×C23 ⋊ C2×D13
HallC13×C23 ⋊ C2×AGL(1,𝔽7)
HallC13×ΓL(1,𝔽8) ⋊ C2×D23
HallC7×C23 ⋊ C2×C3×D13
HallC7×C13 ⋊ C2×C3×D23
SylowC23 ⋊ D13×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ D13×D23
SylowC13 ⋊ AGL(1,𝔽7)×D23
SylowC7 ⋊ C3×D13×D23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C23C22×C3
LCSG ▷ C7×C13×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2093

Polycyclic presentation:

2^2,3,7,13,23|e^a=e^12,f^a=f^22,d^b=d^6,e^b=e^12,d^c=d^4

Conjugacy classes & character table

463 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 75);