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C11×D21×C67 #44526241

order30954
automorphism?
homologyAbelianization (H1) = C2×C11×C67 · Schur multiplier (H2) = C1

Aliases

direct productC11×D21×C67
unambiguous semidirect productC3⋊(C11×D7×C67)
unambiguous semidirect productC7⋊(D3×C11×C67)

Splittings

Fitting, socle, HallC3×C7×C11×C67 ⋊ C2
derived, HallC3×C7 ⋊ C2×C11×C67
HallC7×C11×C67 ⋊ D3
HallC3×C11×C67 ⋊ D7
HallC3×C7×C67 ⋊ C2×C11
HallC7×C67 ⋊ D3×C11
HallC3×C7×C11 ⋊ C2×C67
HallC3×C67 ⋊ C11×D7
HallC7×C11 ⋊ D3×C67
HallC3×C11 ⋊ D7×C67
SylowC7 ⋊ D3×C11×C67
SylowC3 ⋊ C11×D7×C67

Subgroups

subgroupG/H
center, hypercenterC11×C67D21
commutator, cosocle, hypocenterC3×C7C2×C11×C67
FrattiniC1G
Fitting, socleC3×C7×C11×C67C2
LCSG ▷ C3×C7
UCSC1 ◁ C11×C67

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15477

Conjugacy classes & character table

8844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 22);