Finite Group Databasebeta

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C11×C23×Dic15 #29503229

order15180
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C4×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC11×C23×Dic15
unambiguous semidirect productC3⋊(C11×Dic5×C23)

Splittings

derived, HallC3×C5 ⋊ C4×C11×C23
HallC3×C5×C11×C23 ⋊ C4
HallC5×C11×C23 ⋊ Dic3
HallC3×C11×C23 ⋊ Dic5
HallC3×C5×C23 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C23
HallC5×C23 ⋊ C11×Dic3
HallC3×C23 ⋊ C11×Dic5
HallC5×C11 ⋊ Dic3×C23
HallC3×C11 ⋊ Dic5×C23
SylowC5 ⋊ C11×Dic3×C23
SylowC3 ⋊ C11×Dic5×C23

Subgroups

subgroupG/H
center, hypercenterC2×C11×C23D15
commutator, hypocenterC3×C5C4×C11×C23
FrattiniC2C11×C23×D15
Fitting, socle, prime radicalC2×C3×C5×C11×C23C2
cosocleC2×C3×C5C2×C11×C23
LCSG ▷ C3×C5
UCSC1 ◁ C2×C11×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15180

Conjugacy classes & character table

4554 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 15);