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C5×(C23⋊Dic23)⋊C3 #44540693

order31740
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×(C23⋊Dic23)⋊C3
unambiguous semidirect product(C23⋊Dic23)⋊(C3×C5)
unambiguous semidirect product(C5×C23⋊Dic23)⋊C3

Splittings

derived, SylowC232 ⋊ C3×C4×C5
HallC5×C23⋊Dic23 ⋊ C3
HallC5×C232⋊C3 ⋊ C4
HallC5×C232 ⋊ C3×C4
HallC23⋊Dic23 ⋊ C3×C5
HallC232⋊C3 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C5(C23⋊D23)⋊C3
commutator, hypocenterC232C3×C4×C5
FrattiniC2C5×(C23⋊D23)⋊C3
Fitting, socleC2×C5×C232C2×C3
prime radicalC2×C5×C232⋊C3C2
cosocleC2×C232C2×C3×C5
LCSG ▷ C232
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1380

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31740, 31);