Finite Group Databasebeta

← Prev (#72230304) Next (#72230306) →

AGL(1,𝔽5)×#3797 #72230305

order2880
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productAGL(1,𝔽5)×#3797

Splittings

HallC32×C5 ⋊ C2×C4×Q8
SylowC32 ⋊ C2×Q8×AGL(1,𝔽5)
SylowC5 ⋊ C4×#3797

Subgroups

subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C23×C4
FittingC32×C4×C5C22×C4
prime radicalC2×D5×C3⋊D3C23
cosocleC2×C32×D5C24
hypercenterC4D32×AGL(1,𝔽5)
hypocenterC32×C5C2×C4×Q8
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

1300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#64306, AGL(1,𝔽5)×#63930, #72230434, …
maximal normal subgroup ofAGL(1,𝔽5)×#64306, AGL(1,𝔽5)×#63930, #72230434, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.