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C89×ΓL(1,𝔽8)⋊Dic5 #49153129

order37380
automorphism?
homologyAbelianization (H1) = C3×C4×C89 · Schur multiplier (H2) = C1

Aliases

direct productC89×ΓL(1,𝔽8)⋊Dic5
unambiguous semidirect productΓL(1,𝔽8)⋊(Dic5×C89)
unambiguous semidirect productDic35⋊(C3×C89)
unambiguous semidirect product(C89×Dic35)⋊C3

Splittings

derived, HallC5×C7 ⋊ C3×C4×C89
HallC89×Dic35 ⋊ C3
HallC5×ΓL(1,𝔽8)×C89 ⋊ C4
HallC5×C7×C89 ⋊ C3×C4
HallΓL(1,𝔽8)×C89 ⋊ Dic5
HallC7×C89 ⋊ C3×Dic5
HallC5×C89 ⋊ ΓL(1,𝔽8)⋊C4
HallDic35 ⋊ C3×C89
HallC5×ΓL(1,𝔽8) ⋊ C4×C89
HallΓL(1,𝔽8) ⋊ Dic5×C89
SylowC7 ⋊ C3×Dic5×C89
SylowC5 ⋊ ΓL(1,𝔽8)⋊C4×C89

Subgroups

subgroupG/H
center, hypercenterC2×C89C5⋊AGL(1,𝔽7)
commutator, hypocenterC5×C7C3×C4×C89
FrattiniC2C89×C5⋊AGL(1,𝔽7)
Fitting, socleC2×C5×C7×C89C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C89C2
cosocleC2×C5×C7C2×C3×C89
LCSG ▷ C5×C7
UCSC1 ◁ C2×C89

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12460

Conjugacy classes & character table

3026 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 23);