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C2×AGL(1,𝔽7)×C361 #44476453

order30324
automorphism?
homologyAbelianization (H1) = C22×C3×C361 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,𝔽7)×C361
unambiguous semidirect productD7⋊(C2×C3×C361)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C361)
unambiguous semidirect product(C2×D7)⋊(C3×C361)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C361)

Splittings

FittingC2×C7×C361 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C361
HallC2×D7×C361 ⋊ C3
HallΓL(1,𝔽8)×C361 ⋊ C22
HallC7×C361 ⋊ C22×C3
HallC2×D7 ⋊ C3×C361
HallΓL(1,𝔽8) ⋊ C22×C361

Subgroups

subgroupG/H
center, hypercenterC2×C361AGL(1,𝔽7)
commutator, hypocenterC7C22×C3×C361
FrattiniC19C2×C19×AGL(1,𝔽7)
FittingC2×C7×C361C2×C3
socleC2×C7×C19C2×C3×C19
prime radicalC2×C19×AGL(1,𝔽7)C19
cosocleC7×C19C22×C3×C19
LCSG ▷ C7
UCSC1 ◁ C2×C361

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5054

Conjugacy classes & character table

5054 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30324, 36);