Finite Group Databasebeta

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C3×C11×Dic5×C23 #29503221

order15180
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic5×C23

Splittings

derived, SylowC5 ⋊ C3×C4×C11×C23
HallC3×C5×C11×C23 ⋊ C4
HallC5×C11×C23 ⋊ C3×C4
HallC3×C5×C23 ⋊ C4×C11
HallC3×C5×C11 ⋊ C4×C23
HallC5×C23 ⋊ C3×C4×C11
HallC5×C11 ⋊ C3×C4×C23
HallC3×C5 ⋊ C4×C11×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C23D5
commutator, hypocenterC5C3×C4×C11×C23
FrattiniC2C3×D5×C11×C23
Fitting, socle, prime radicalC2×C3×C5×C11×C23C2
cosocleC2×C5C2×C3×C11×C23
LCSG ▷ C5
UCSC1 ◁ C2×C3×C11×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15180

Conjugacy classes & character table

6072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 7);