Finite Group Databasebeta

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C3×D17×C23⋊C11 #38788747

order25806
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×D17×C23⋊C11
unambiguous semidirect productC17⋊(C2×C3×C23⋊C11)
unambiguous semidirect product(C23×D17)⋊(C3×C11)
unambiguous semidirect product(C3×C23×D17)⋊C11

Splittings

Fitting, socle, HallC3×C17×C23 ⋊ C2×C11
derived, HallC17×C23 ⋊ C2×C3×C11
HallC3×C17×C23⋊C11 ⋊ C2
HallC17×C23⋊C11 ⋊ C2×C3
HallC3×C23×D17 ⋊ C11
HallC23×D17 ⋊ C3×C11
HallC3×C23 ⋊ C11×D17
HallC3×C17 ⋊ C2×C23⋊C11
SylowC23 ⋊ C3×C11×D17
SylowC17 ⋊ C2×C3×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC3D17×C23⋊C11
commutator, cosocle, hypocenterC17×C23C2×C3×C11
FrattiniC1G
Fitting, socleC3×C17×C23C2×C11
LCSG ▷ C17×C23
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1173

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25806, 19);