Finite Group Databasebeta

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#379×#1043 #72258494

order6400
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct product#379×#1043

Splittings

FittingC52×#379 ⋊ C4
SylowC52 ⋊ C4×#379

Subgroups

subgroupG/H
center, FrattiniC23C23×#1043
commutatorC22×C52C22×C42
FittingC52×#379C4
socleC23×C52C23×C4
prime radicalC25×C5⋊D5C22
cosocleC23×C5⋊D5C24
hypercenter#379#1043
hypocenterC52C4×#379
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ #379

26936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.