Finite Group Databasebeta

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C2×C23×C49⋊C9 #35202542

order20286
automorphism?
homologyAbelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC2×C23×C49⋊C9
unambiguous semidirect product(C2×C49)⋊(C9×C23)
unambiguous semidirect product(C2×C23×C49)⋊C9

Splittings

derived, SylowC49 ⋊ C2×C9×C23
HallC2×C23×C49 ⋊ C9
HallC23×C49 ⋊ C2×C9
HallC2×C49 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23C49⋊C3
commutator, hypocenterC49C2×C9×C23
FrattiniC3×C7C2×ΓL(1,𝔽8)×C23
FittingC2×C3×C23×C49C3
socle, prime radicalC2×C3×C7×C23ΓL(1,𝔽8)
cosocleC3×C49C2×C3×C23
LCSG ▷ C49
UCSC1 ◁ C2×C3×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20286

Conjugacy classes & character table

2622 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20286, 5);