Finite Group Databasebeta

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C5×C23×D39 #22582241

order8970
isoclinismisoclinic class of D39
automorphism?
homologyAbelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×D39
unambiguous semidirect productC3⋊(C5×C23×D13)
unambiguous semidirect productC13⋊(C5×D3×C23)

Splittings

Fitting, socle, HallC3×C5×C13×C23 ⋊ C2
derived, HallC3×C13 ⋊ C2×C5×C23
HallC5×C13×C23 ⋊ D3
HallC3×C13×C23 ⋊ C2×C5
HallC3×C5×C23 ⋊ D13
HallC13×C23 ⋊ C5×D3
HallC3×C5×C13 ⋊ C2×C23
HallC3×C23 ⋊ C5×D13
HallC5×C13 ⋊ D3×C23
HallC3×C5 ⋊ C23×D13
SylowC13 ⋊ C5×D3×C23
SylowC3 ⋊ C5×C23×D13

Subgroups

subgroupG/H
center, hypercenterC5×C23D39
commutator, hypocenterC3×C13C2×C5×C23
FrattiniC1G
Fitting, socleC3×C5×C13×C23C2
LCSG ▷ C3×C13
UCSC1 ◁ C5×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2415 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D23×D39, C5×D3×C23×D13, C5×D39⋊D23, …
maximal normal subgroup ofC5×D23×D39, C5×D3×C23×D13, C5×D39⋊D23, …
maximal quotient ofC5×C23×Dic39, C2×C5×C23×D39, C5×C23×D117, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8970, 12);