Finite Group Databasebeta

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D7×C22⋊#1044 #72243109

order5600
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C5

Aliases

direct productD7×C22⋊#1044

Splittings

FittingC22×C52×C7 ⋊ C2×C4
HallC52×C7 ⋊ C2×C22⋊C4
SylowC52 ⋊ D7×C22⋊C4
SylowC7 ⋊ C2×C22⋊#1044

Subgroups

subgroupG/H
center, FrattiniC2C2×D7×#1044
commutator, socleC2×C52×C7C22×C4
FittingC22×C52×C7C2×C4
prime radicalC22×D7×C5⋊D5C2
cosocleC2×C7×C5⋊D5C23
hypercenterC22D7×#1044
hypocenterC52×C7C2×C22⋊C4
LCSG ▷ C2×C52×C7 ▷ C52×C7
UCSC1 ◁ C2 ◁ C22

796 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 796 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 140

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×#11717375, AGL(1,𝔽7)×C22⋊#1044
maximal normal subgroup ofD7×#11717375, AGL(1,𝔽7)×C22⋊#1044

GAP

Past the SmallGroups library coverage — no SmallGroups id.