Finite Group Databasebeta

← Prev (#72277284) Next (#72277286) →

C2×C3×#11716761 #72277285

order4800
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C3×#11716761

Splittings

derived, SylowC52 ⋊ C2×C3×C4×C8
HallC3×C52 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4D5⋊AGL(1,𝔽5)
commutator, hypocenterC52C2×C3×C4×C8
FrattiniC4C2×C3×D5⋊AGL(1,𝔽5)
FittingC2×C3×C4×C52C2×C4
socleC22×C3×C52C42
prime radicalC22×C3×C5⋊D5C2×C4
cosocleC4×C5⋊D5C23×C3
LCSG ▷ C52
UCSC1 ◁ C2×C3×C4

864 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.