Finite Group Databasebeta

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D51×C23⋊C11 #38788751

order25806
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productD51×C23⋊C11
unambiguous semidirect productC3⋊(D17×C23⋊C11)
unambiguous semidirect productC17⋊(D3×C23⋊C11)
unambiguous semidirect product(C23×D51)⋊C11

Splittings

Fitting, socle, derived, HallC3×C17×C23 ⋊ C2×C11
HallC3×C17×C23⋊C11 ⋊ C2
HallC17×C23⋊C11 ⋊ D3
HallC23×D51 ⋊ C11
HallC3×C23⋊C11 ⋊ D17
HallC17×C23 ⋊ D3×C11
HallC3×C23 ⋊ C11×D17
HallC3×C17 ⋊ C2×C23⋊C11
SylowC23 ⋊ C11×D51
SylowC17 ⋊ D3×C23⋊C11
SylowC3 ⋊ D17×C23⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C17×C23C2×C11
LCSG ▷ C3×C17×C23
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1173

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25806, 23);