Finite Group Databasebeta

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AGL(1,𝔽7)×#11717375 #72243239

order33600
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productAGL(1,𝔽7)×#11717375

Splittings

FittingC22×C52×C7 ⋊ C22×C3×C4
HallD7×#11717375 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ C2×C4×D4
HallC52×C7 ⋊ C2×C3×C4×D4
SylowC52 ⋊ C4×D4×AGL(1,𝔽7)
HallΓL(1,𝔽8) ⋊ C2×#11717375
SylowC7 ⋊ C2×C3×#11717375

Subgroups

subgroupG/H
center, FrattiniC2C2×AGL(1,𝔽7)×D5⋊AGL(1,𝔽5)
commutator, socleC2×C52×C7C23×C3×C4
FittingC22×C52×C7C22×C3×C4
prime radicalAGL(1,𝔽7)×#87886C2
cosocleC2×C7×C5⋊D5C24×C3
hypercenterC22AGL(1,𝔽7)×D5⋊AGL(1,𝔽5)
hypocenterC52×C7C2×C3×C4×D4
LCSG ▷ C2×C52×C7 ▷ C52×C7
UCSC1 ◁ C2 ◁ C22

4352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 140

Conjugacy classes & character table

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

Relationships

holomorph ofC7×Dic5, C2×C7×D5

GAP

Past the SmallGroups library coverage — no SmallGroups id.