Finite Group Databasebeta

← Prev (#72253113) Next (#72253115) →

C5⋊D5×#12067 #72253114

order12800
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26×C5

Aliases

direct productC5⋊D5×#12067

Splittings

FittingC52×#12067 ⋊ C2
SylowC52 ⋊ C2×#12067

Subgroups

subgroupG/H
centerC22C5⋊D5×#442
commutatorC52×C8C23×C8
FrattiniC4×C8C23×C5⋊D5
FittingC52×#12067C2
socleC22×C52C2×#442
prime radicalC2×D16×C5⋊D5C4
cosocleC4×C52×C8C24
hypercenter#12067C5⋊D5
hypocenterC52C2×#12067
LCSG ▷ C52×C8 ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C42 ◁ #322 ◁ #12067

4624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3200

Conjugacy classes & character table

644 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.