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AGL(1,𝔽7)×D5⋊C8 #72217468

order3360
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productAGL(1,𝔽7)×D5⋊C8

Splittings

derived, HallC5×C7 ⋊ C22×C3×C8
HallD7×D5⋊C8 ⋊ C3
HallC5×ΓL(1,𝔽8) ⋊ C22×C8
HallΓL(1,𝔽8) ⋊ C2×D5⋊C8
SylowC7 ⋊ C2×C3×D5⋊C8
SylowC5 ⋊ C2×C8×AGL(1,𝔽7)

Subgroups

subgroupG/H
center, hypercenterC4AGL(1,𝔽5)×AGL(1,𝔽7)
commutator, hypocenterC5×C7C22×C3×C8
FrattiniC2C2×AGL(1,𝔽5)×AGL(1,𝔽7)
FittingC4×C5×C7C2×C3×C4
socleC2×C5×C7C22×C3×C4
prime radicalC2×D5×AGL(1,𝔽7)C4
cosocleC7×Dic5C23×C3
LCSG ▷ C5×C7
UCSC1 ◁ C4

304 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D5⋊AGL(1,𝔽9), C8×AGL(1,𝔽5)×AGL(1,𝔽7), AGL(1,𝔽7)×#3992, …
maximal normal subgroup ofC8×AGL(1,𝔽5)×AGL(1,𝔽7), AGL(1,𝔽7)×#3992, AGL(1,𝔽7)×D5⋊M16, …
maximal quotient ofAGL(1,𝔽7)×D5⋊AGL(1,𝔽9)

GAP

Past the SmallGroups library coverage — no SmallGroups id.