Finite Group Databasebeta

← Prev (#72222625) Next (#72222627) →

D32×D5⋊AGL(1,𝔽5) #72222626

order7200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD32×D5⋊AGL(1,𝔽5)

Splittings

Fitting, socle, derived, HallC32×C52 ⋊ C23×C4
SylowC52 ⋊ C2×C4×D32
SylowC32 ⋊ C22×D5⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C52C23×C4
prime radicalD32×D52C2
cosocleC32×C5⋊D5C24
LCSG ▷ C32×C52
UCSC1

2228 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72210392, D32×AGL(1,𝔽5)2, D3×C3⋊D3×D5⋊AGL(1,𝔽5), …
maximal normal subgroup ofD32×AGL(1,𝔽5)2, C2×D32×D5⋊AGL(1,𝔽5)
maximal quotient ofD3×#72210392, D3×C3⋊D3×D5⋊AGL(1,𝔽5), C2×D32×D5⋊AGL(1,𝔽5)
holomorph ofD3×D5

GAP

Past the SmallGroups library coverage — no SmallGroups id.