Finite Group Databasebeta

← Prev (#37613380) Next (#37613382) →

C2×ΓL(1,𝔽8)×D295 #37613381

order24780
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×ΓL(1,𝔽8)×D295
unambiguous semidirect product(C2×C5)⋊(ΓL(1,𝔽8)×D59)
unambiguous semidirect product(C2×C59)⋊(D5×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D295)⋊C3

Splittings

Fitting, socleC2×C5×C7×C59 ⋊ C2×C3
derived, HallC5×C7×C59 ⋊ C22×C3
HallC2×C7×D295 ⋊ C3
HallC5×ΓL(1,𝔽8)×C59 ⋊ C22
HallΓL(1,𝔽8)×C59 ⋊ C2×D5
HallC7×C59 ⋊ C2×C3×D5
HallC5×C59 ⋊ C22×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ C2×D59
SylowC59 ⋊ C2×D5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C3×D59
SylowC7 ⋊ C2×C3×D295
SylowC5 ⋊ C2×ΓL(1,𝔽8)×D59

Subgroups

subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×D295
commutator, cosocle, hypocenterC5×C7×C59C22×C3
FrattiniC1G
Fitting, socleC2×C5×C7×C59C2×C3
LCSG ▷ C5×C7×C59
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4130

Conjugacy classes & character table

1490 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 43);