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C5×C7×C9×D23 #28408012

order14490
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C9×D23
unambiguous semidirect productC23⋊(C2×C5×C7×C9)

Splittings

Fitting, HallC5×C7×C9×C23 ⋊ C2
derived, SylowC23 ⋊ C2×C5×C7×C9
HallC7×C9×C23 ⋊ C2×C5
HallC5×C9×C23 ⋊ C2×C7
HallC5×C7×C23 ⋊ C2×C9
HallC9×C23 ⋊ C2×C5×C7
HallC7×C23 ⋊ C2×C5×C9
HallC5×C23 ⋊ C2×C7×C9

Subgroups

subgroupG/H
center, hypercenterC5×C7×C9D23
commutator, hypocenterC23C2×C5×C7×C9
FrattiniC3C3×C5×C7×D23
FittingC5×C7×C9×C23C2
socleC3×C5×C7×C23C2×C3
prime radicalC3×C5×C7×D23C3
cosocleC3×C23C2×C3×C5×C7
LCSG ▷ C23
UCSC1 ◁ C5×C7×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7245

Conjugacy classes & character table

4095 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×D7×D23, C7×C9×D5×D23, C9×D23×D35, …
maximal normal subgroup ofC5×C9×D7×D23, C7×C9×D5×D23, C9×D23×D35, …
maximal quotient ofC5×C7×C9×Dic23, C2×C5×C7×C9×D23

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 3);