Finite Group Databasebeta

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#1043×#1333 #72253187

order12800
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct product#1043×#1333

Splittings

FittingC52×#1333 ⋊ C4
SylowC52 ⋊ C4×#1333

Subgroups

subgroupG/H
centerC22#102×#1043
commutatorC52×C8C2×C4×C8
FrattiniC4×C8C22×#1043
FittingC52×#1333C4
socleC22×C52C4×#102
prime radicalC2×D8×C5⋊D5C2×C4
cosocleC4×C8×C5⋊D5C23
hypercenter#1333#1043
hypocenterC52C4×#1333
LCSG ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1333

4160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1600

Conjugacy classes & character table

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

Relationships

maximal subgroup of#1043×#12067
maximal normal subgroup of#1043×#12067

GAP

Past the SmallGroups library coverage — no SmallGroups id.