Finite Group Databasebeta

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C3×C13×D11×C25 #36339682

order21450
automorphism?
homologyAbelianization (H1) = C2×C3×C13×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×D11×C25

Splittings

Fitting, HallC3×C11×C13×C25 ⋊ C2
derived, SylowC11 ⋊ C2×C3×C13×C25
HallC11×C13×C25 ⋊ C2×C3
HallC3×C11×C25 ⋊ C2×C13
HallC3×C11×C13 ⋊ C2×C25
HallC11×C25 ⋊ C2×C3×C13
HallC11×C13 ⋊ C2×C3×C25
HallC3×C11 ⋊ C2×C13×C25

Subgroups

subgroupG/H
center, hypercenterC3×C13×C25D11
commutator, hypocenterC11C2×C3×C13×C25
FrattiniC5C3×C5×C13×D11
FittingC3×C11×C13×C25C2
socleC3×C5×C11×C13C2×C5
prime radicalC3×C5×C13×D11C5
cosocleC5×C11C2×C3×C5×C13
LCSG ▷ C11
UCSC1 ◁ C3×C13×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10725

Conjugacy classes & character table

6825 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 6);