Finite Group Databasebeta

← Prev (#72242680) Next (#72242682) →

C22×C42×#1043 #72242681

order6400
automorphism?
homologyAbelianization (H1) = C22×C43 · Schur multiplier (H2) = C27×C43

Aliases

direct productC22×C42×#1043

Splittings

FittingC22×C42×C52 ⋊ C4
derived, SylowC52 ⋊ C22×C43

Subgroups

subgroupG/H
center, hypercenterC22×C42#1043
commutator, hypocenterC52C22×C43
FrattiniC22C24×#1043
FittingC22×C42×C52C4
socleC24×C52C22×C4
prime radicalC24×C5⋊D5C23
cosocleC22×C5⋊D5C25
LCSG ▷ C52
UCSC1 ◁ C22×C42

32376 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1600

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22×#72220669
maximal normal subgroup ofC22×#72220669

GAP

Past the SmallGroups library coverage — no SmallGroups id.