Finite Group Databasebeta

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C4×C47×C7⋊C9 #26044858

order11844
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C4×C9×C47 · Schur multiplier (H2) = C1

Aliases

direct productC4×C47×C7⋊C9
unambiguous semidirect product(C4×C7)⋊(C9×C47)
unambiguous semidirect product(C4×C7×C47)⋊C9

Splittings

derived, SylowC7 ⋊ C4×C9×C47
HallC4×C7×C47 ⋊ C9
HallC7×C47 ⋊ C4×C9
HallC4×C7 ⋊ C9×C47

Subgroups

subgroupG/H
center, hypercenterC3×C4×C47ΓL(1,𝔽8)
commutator, hypocenterC7C4×C9×C47
FrattiniC2×C3C2×ΓL(1,𝔽8)×C47
FittingC3×C4×C7×C47C3
socle, prime radicalC2×C3×C7×C47C2×C3
cosocleC2×C3×C7C2×C3×C47
LCSG ▷ C7
UCSC1 ◁ C3×C4×C47

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11844, 5);