Finite Group Databasebeta

← Prev (#72243115) Next (#72243117) →

D7×#11717375 #72243116

order11200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD7×#11717375

Splittings

FittingC22×C52×C7 ⋊ C22×C4
HallC52×C7 ⋊ C2×C4×D4
SylowC52 ⋊ C4×D4×D7
SylowC7 ⋊ C2×#11717375

Subgroups

subgroupG/H
center, FrattiniC2C2×D7×D5⋊AGL(1,𝔽5)
commutator, socleC2×C52×C7C23×C4
FittingC22×C52×C7C22×C4
prime radicalD7×#87886C2
cosocleC2×C7×C5⋊D5C24
hypercenterC22D7×D5⋊AGL(1,𝔽5)
hypocenterC52×C7C2×C4×D4
LCSG ▷ C2×C52×C7 ▷ C52×C7
UCSC1 ◁ C2 ◁ C22

2176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 140

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#11717375
maximal normal subgroup ofAGL(1,𝔽7)×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.