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C13×C23×D15 #22582243

order8970
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C2×C13×C23 · Schur multiplier (H2) = C1

Aliases

direct productC13×C23×D15
unambiguous semidirect productC3⋊(D5×C13×C23)
unambiguous semidirect productC5⋊(D3×C13×C23)

Splittings

Fitting, socle, HallC3×C5×C13×C23 ⋊ C2
derived, HallC3×C5 ⋊ C2×C13×C23
HallC5×C13×C23 ⋊ D3
HallC3×C13×C23 ⋊ D5
HallC3×C5×C23 ⋊ C2×C13
HallC3×C5×C13 ⋊ C2×C23
HallC5×C23 ⋊ D3×C13
HallC3×C23 ⋊ D5×C13
HallC5×C13 ⋊ D3×C23
HallC3×C13 ⋊ D5×C23
SylowC5 ⋊ D3×C13×C23
SylowC3 ⋊ D5×C13×C23

Subgroups

subgroupG/H
center, hypercenterC13×C23D15
commutator, hypocenterC3×C5C2×C13×C23
FrattiniC1G
Fitting, socleC3×C5×C13×C23C2
LCSG ▷ C3×C5
UCSC1 ◁ C13×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2691 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×D15×D23, C23×D13×D15, D15×D299, …
maximal normal subgroup ofC13×D15×D23, C23×D13×D15, D15×D299, …
maximal quotient ofC13×C23×Dic15, C2×C13×C23×D15, C13×C23×D45, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8970, 14);