Finite Group Databasebeta

← Prev (#72246301) Next (#72246303) →

#453×ΓL(1,𝔽8)⋊D7 #72246302

order18816
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct product#453×ΓL(1,𝔽8)⋊D7

Splittings

FittingC72×#453 ⋊ C2×C3
Hall#453×C7⋊D7 ⋊ C3
HallC7×ΓL(1,𝔽8) ⋊ C2×#453
SylowC72 ⋊ C2×C3×#453

Subgroups

subgroupG/H
centerC2#120×ΓL(1,𝔽8)⋊D7
commutator, cosocleC2×C4×C72C24×C3
FrattiniC2×C4C23×ΓL(1,𝔽8)⋊D7
FittingC72×#453C2×C3
socleC2×C72C2×C3×#120
hypercenter#453ΓL(1,𝔽8)⋊D7
hypocenterC72C2×C3×#453
LCSG ▷ C2×C4×C72 ▷ C2×C72 ▷ C72
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

4220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

352 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.