Finite Group Databasebeta

← Prev (#72243262) Next (#72243264) →

C2×AGL(1,𝔽5)×#3861 #72243263

order5880
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,𝔽5)×#3861

Splittings

Fitting, socleC2×C5×C72 ⋊ C3×C4
derived, HallC5×C72 ⋊ C2×C3×C4
HallC2×C72×AGL(1,𝔽5) ⋊ C3
HallC5×#3861 ⋊ C2×C4
SylowC72 ⋊ C2×C3×AGL(1,𝔽5)
SylowC5 ⋊ C2×C4×#3861

Subgroups

subgroupG/H
center, hypercenterC2AGL(1,𝔽5)×#3861
commutator, hypocenterC5×C72C2×C3×C4
FrattiniC1G
Fitting, socleC2×C5×C72C3×C4
prime radicalC2×D5×#3861C2
cosocleC72×D5C22×C3
LCSG ▷ C5×C72
UCSC1 ◁ C2

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 490

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#64424, C22×AGL(1,𝔽5)×#3861, C2×AGL(1,𝔽5)×#64423, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#64424, C22×AGL(1,𝔽5)×#3861, C2×AGL(1,𝔽5)×#64423, …
maximal quotient ofC22×AGL(1,𝔽5)×#3861

GAP

Past the SmallGroups library coverage — no SmallGroups id.