Finite Group Databasebeta

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C7×C23×D45 #28408023

order14490
isoclinismisoclinic class of D45
automorphism?
homologyAbelianization (H1) = C2×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23×D45
unambiguous semidirect productC5⋊(C7×D9×C23)
unambiguous semidirect productC9⋊(C7×D5×C23)

Splittings

Fitting, HallC5×C7×C9×C23 ⋊ C2
derived, HallC5×C9 ⋊ C2×C7×C23
HallC7×C9×C23 ⋊ D5
HallC5×C9×C23 ⋊ C2×C7
HallC5×C7×C23 ⋊ D9
HallC5×C7×C9 ⋊ C2×C23
HallC9×C23 ⋊ C7×D5
HallC5×C23 ⋊ C7×D9
HallC7×C9 ⋊ D5×C23
HallC5×C7 ⋊ D9×C23
SylowC9 ⋊ C7×D5×C23
SylowC5 ⋊ C7×D9×C23

Subgroups

subgroupG/H
center, hypercenterC7×C23D45
commutator, cosocle, hypocenterC5×C9C2×C7×C23
FrattiniC3C7×C23×D15
FittingC5×C7×C9×C23C2
socleC3×C5×C7×C23D3
LCSG ▷ C5×C9
UCSC1 ◁ C7×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7245

Conjugacy classes & character table

3864 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D23×D45, D7×C23×D45, D45×D161, …
maximal normal subgroup ofC7×D23×D45, D7×C23×D45, D45×D161, …
maximal quotient ofC7×C23×Dic45, C2×C7×C23×D45

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 14);