Finite Group Databasebeta

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C4×C17×C23⋊C11 #31769958

order17204
isoclinismisoclinic class of C23⋊C11
automorphism?
homologyAbelianization (H1) = C4×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C17×C23⋊C11
unambiguous semidirect product(C4×C23)⋊(C11×C17)
unambiguous semidirect product(C4×C17×C23)⋊C11

Splittings

Fitting, HallC4×C17×C23 ⋊ C11
derived, SylowC23 ⋊ C4×C11×C17
HallC17×C23 ⋊ C4×C11
HallC4×C23 ⋊ C11×C17

Subgroups

subgroupG/H
center, hypercenterC4×C17C23⋊C11
commutator, hypocenterC23C4×C11×C17
FrattiniC2C2×C17×C23⋊C11
FittingC4×C17×C23C11
socleC2×C17×C23C2×C11
prime radicalC2×C17×C23⋊C11C2
cosocleC2×C23C2×C11×C17
LCSG ▷ C23
UCSC1 ◁ C4×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1564

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17204, 2);