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#104×ΓL(1,𝔽8)⋊D7 #72246284

order9408
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct product#104×ΓL(1,𝔽8)⋊D7

Splittings

FittingC72×#104 ⋊ C2×C3
Hall#104×C7⋊D7 ⋊ C3
HallC7×ΓL(1,𝔽8) ⋊ C2×#104
SylowC72 ⋊ C2×C3×#104

Subgroups

subgroupG/H
centerC4D4×ΓL(1,𝔽8)⋊D7
commutatorC4×C72C22×C3×C4
FrattiniC2×C4C22×ΓL(1,𝔽8)⋊D7
FittingC72×#104C2×C3
socleC2×C72C2×C3×C22⋊C4
prime radical#41×ΓL(1,𝔽8)⋊D7C2
cosocleC2×C4×C72C23×C3
hypercenter#104ΓL(1,𝔽8)⋊D7
hypocenterC72C2×C3×#104
LCSG ▷ C4×C72 ▷ C2×C72 ▷ C72
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

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

Relationships

maximal subgroup of#453×ΓL(1,𝔽8)⋊D7, #104×ΓL(1,𝔽8)⋊AGL(1,𝔽7)
maximal normal subgroup of#453×ΓL(1,𝔽8)⋊D7, #104×ΓL(1,𝔽8)⋊AGL(1,𝔽7)

GAP

Past the SmallGroups library coverage — no SmallGroups id.