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#100×ΓL(1,𝔽8)⋊AGL(1,𝔽7) #72246369

order28224
automorphism?
homologyAbelianization (H1) = C22×C32×C4 · Schur multiplier (H2) = C23×C3

Aliases

direct product#100×ΓL(1,𝔽8)⋊AGL(1,𝔽7)

Splittings

FittingC72×#100 ⋊ C2×C32
Hall#100×C7⋊D7 ⋊ C32
HallΓL(1,𝔽8)2 ⋊ C2×#100
SylowC72 ⋊ C2×C32×#100

Subgroups

subgroupG/H
centerC2C22⋊C4×ΓL(1,𝔽8)⋊AGL(1,𝔽7)
commutatorC22×C72C22×C32×C4
FrattiniC2×C4C22×ΓL(1,𝔽8)⋊AGL(1,𝔽7)
FittingC72×#100C2×C32
socleC2×C72C2×C32×C22⋊C4
prime radicalC2×D4×ΓL(1,𝔽8)⋊AGL(1,𝔽7)C2
cosocleC2×C4×C72C23×C32
hypercenter#100ΓL(1,𝔽8)⋊AGL(1,𝔽7)
hypocenterC72C2×C32×#100
LCSG ▷ C22×C72 ▷ C2×C72 ▷ C72
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

2604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

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

Relationships

maximal subgroup of#453×ΓL(1,𝔽8)⋊AGL(1,𝔽7)
maximal normal subgroup of#453×ΓL(1,𝔽8)⋊AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.