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C24×C4×AGL(1,𝔽7) #72218461

order2688
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C25×C3×C4 · Schur multiplier (H2) = C215

Aliases

direct productC24×C4×AGL(1,𝔽7)

Splittings

FittingC24×C4×C7 ⋊ C2×C3
derived, SylowC7 ⋊ C25×C3×C4
HallC24×C4×D7 ⋊ C3
HallΓL(1,𝔽8) ⋊ C25×C4

Subgroups

subgroupG/H
center, hypercenterC24×C4AGL(1,𝔽7)
commutator, hypocenterC7C25×C3×C4
FrattiniC2C25×AGL(1,𝔽7)
FittingC24×C4×C7C2×C3
socleC25×C7C22×C3
prime radicalC25×AGL(1,𝔽7)C2
cosocleC2×C7C26×C3
LCSG ▷ C7
UCSC1 ◁ C24×C4

21104 conjugacy classes of subgroups; only the 11233 normal subgroups are shown.

normal subgroups only

This group has 21104 conjugacy classes of subgroups — too many to draw. Only its 11233 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

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

Relationships

maximal subgroup ofC24×AGL(1,𝔽5)×AGL(1,𝔽7), C4×#120×AGL(1,𝔽7)
maximal normal subgroup ofC4×#120×AGL(1,𝔽7)
maximal quotient ofC24×AGL(1,𝔽5)×AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.