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C4×C5×ΓL(1,𝔽8)×C89 #49153108

order37380
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C89 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×ΓL(1,𝔽8)×C89
unambiguous semidirect product(C4×C7)⋊(C3×C5×C89)
unambiguous semidirect product(C4×C5×C7)⋊(C3×C89)
unambiguous semidirect product(C4×C7×C89)⋊(C3×C5)
unambiguous semidirect product(C4×C5×C7×C89)⋊C3

Splittings

Fitting, HallC4×C5×C7×C89 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C5×C89
HallC5×C7×C89 ⋊ C3×C4
HallC4×C7×C89 ⋊ C3×C5
HallC7×C89 ⋊ C3×C4×C5
HallC4×C5×C7 ⋊ C3×C89
HallC5×C7 ⋊ C3×C4×C89
HallC4×C7 ⋊ C3×C5×C89

Subgroups

subgroupG/H
center, hypercenterC4×C5×C89ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C5×C89
FrattiniC2C2×C5×ΓL(1,𝔽8)×C89
FittingC4×C5×C7×C89C3
socleC2×C5×C7×C89C2×C3
prime radicalC2×C5×ΓL(1,𝔽8)×C89C2
cosocleC2×C7C2×C3×C5×C89
LCSG ▷ C7
UCSC1 ◁ C4×C5×C89

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12460

Conjugacy classes & character table

8900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 2);