Finite Group Databasebeta

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#1043×#12067 #72269142

order25600
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct product#1043×#12067

Splittings

FittingC52×#12067 ⋊ C4
SylowC52 ⋊ C4×#12067

Subgroups

subgroupG/H
centerC22#442×#1043
commutatorC52×C8C22×C4×C8
FrattiniC4×C8C23×#1043
FittingC52×#12067C4
socleC22×C52C4×#442
prime radicalC2×D16×C5⋊D5C2×C4
cosocleC4×C8×C5⋊D5C24
hypercenter#12067#1043
hypocenterC52C4×#12067
LCSG ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #12067

10792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3200

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.