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C5×ΓL(1,𝔽8)×Dic89 #49153124

order37380
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×Dic89
unambiguous semidirect product(C7×Dic89)⋊(C3×C5)
unambiguous semidirect product(C5×C7×Dic89)⋊C3

Splittings

derived, HallC7×C89 ⋊ C3×C4×C5
HallC5×C7×Dic89 ⋊ C3
HallC5×ΓL(1,𝔽8)×C89 ⋊ C4
HallC5×C7×C89 ⋊ C3×C4
HallC7×Dic89 ⋊ C3×C5
HallΓL(1,𝔽8)×C89 ⋊ C4×C5
HallC5×C89 ⋊ C4×ΓL(1,𝔽8)
SylowC89 ⋊ C4×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×Dic89
SylowC7 ⋊ C3×C5×Dic89

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)×D89
commutator, hypocenterC7×C89C3×C4×C5
FrattiniC2C5×ΓL(1,𝔽8)×D89
Fitting, socleC2×C5×C7×C89C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C89C2
cosocleC2×C7×C89C2×C3×C5
LCSG ▷ C7×C89
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12460

Conjugacy classes & character table

2300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 18);