Finite Group Databasebeta

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D32×#64423⋊C2 #72222193

order21168
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productD32×#64423⋊C2

Splittings

Fitting, socle, derivedC32×C72 ⋊ C24×C3
HallC32×#3861 ⋊ C24
SylowC72 ⋊ C22×C3×D32

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C72C24×C3
LCSG ▷ C32×C72
UCSC1

3054 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#72213636
maximal quotient ofD3×#72213636
holomorph ofD3×D7

GAP

Past the SmallGroups library coverage — no SmallGroups id.