Finite Group Databasebeta

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D2233 #17985000

order4466
automorphismAut(G) order 3751440
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD2233
unambiguous semidirect productC7⋊D319
unambiguous semidirect productC11⋊D203
unambiguous semidirect productC29⋊D77

Splittings

Fitting, socle, derived, HallC7×C11×C29 ⋊ C2
HallC11×C29 ⋊ D7
HallC7×C29 ⋊ D11
HallC7×C11 ⋊ D29
SylowC29 ⋊ D77
SylowC11 ⋊ D203
SylowC7 ⋊ D319

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C29C2
LCSG ▷ C7×C11×C29
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 2233

Polycyclic presentation:

2,7,11,29|b^a=b^6,c^a=c^10,d^a=d^28

Conjugacy classes & character table

1118 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D2233, D6699, C11⋊(ΓL(1,𝔽8)⋊D29), …
maximal normal subgroup ofC3×D2233, C11⋊(ΓL(1,𝔽8)⋊D29), C5×D2233, …
maximal quotient ofC3×D2233, D6699, C5×D2233, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4466, 9);