Finite Group Databasebeta

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C5×C23×Dic33 #29503227

order15180
isoclinismisoclinic class of D33
automorphism?
homologyAbelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×Dic33
unambiguous semidirect productC3⋊(C5×C23×Dic11)

Splittings

derived, HallC3×C11 ⋊ C4×C5×C23
HallC3×C5×C11×C23 ⋊ C4
HallC5×C11×C23 ⋊ Dic3
HallC3×C11×C23 ⋊ C4×C5
HallC3×C5×C23 ⋊ Dic11
HallC11×C23 ⋊ C5×Dic3
HallC3×C5×C11 ⋊ C4×C23
HallC3×C23 ⋊ C5×Dic11
HallC5×C11 ⋊ Dic3×C23
HallC3×C5 ⋊ C23×Dic11
SylowC11 ⋊ C5×Dic3×C23
SylowC3 ⋊ C5×C23×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C23D33
commutator, hypocenterC3×C11C4×C5×C23
FrattiniC2C5×C23×D33
Fitting, socle, prime radicalC2×C3×C5×C11×C23C2
cosocleC2×C3×C11C2×C5×C23
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15180

Conjugacy classes & character table

4140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 13);