Finite Group Databasebeta

← Prev (#49153133) Next (#49153135) →

C5×ΓL(1,𝔽8)×#67063 #49153134

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

Aliases

direct productC5×ΓL(1,𝔽8)×#67063
unambiguous semidirect product(C7×#67063)⋊(C3×C5)
unambiguous semidirect product(C5×C7×#67063)⋊C3

Splittings

Fitting, socle, HallC5×C7×C89 ⋊ C3×C4
derived, HallC7×C89 ⋊ C3×C4×C5
HallC5×C7×#67063 ⋊ C3
HallC5×ΓL(1,𝔽8)×C89 ⋊ C4
HallC7×#67063 ⋊ C3×C5
HallΓL(1,𝔽8)×C89 ⋊ C4×C5
HallC5×C89 ⋊ C4×ΓL(1,𝔽8)
SylowC89 ⋊ C4×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×#67063
SylowC7 ⋊ C3×C5×#67063

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×#67063
commutator, hypocenterC7×C89C3×C4×C5
FrattiniC1G
Fitting, socleC5×C7×C89C3×C4
prime radicalC5×ΓL(1,𝔽8)×D89C2
cosocleC7×D89C2×C3×C5
LCSG ▷ C7×C89
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3115

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 28);