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C67×D231 #44526243

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

Aliases

direct productC67×D231
unambiguous semidirect productC3⋊(C67×D77)
unambiguous semidirect productC7⋊(D33×C67)
unambiguous semidirect productC11⋊(D21×C67)

Splittings

Fitting, socle, HallC3×C7×C11×C67 ⋊ C2
derived, HallC3×C7×C11 ⋊ C2×C67
HallC7×C11×C67 ⋊ D3
HallC3×C11×C67 ⋊ D7
HallC3×C7×C67 ⋊ D11
HallC11×C67 ⋊ D21
HallC7×C67 ⋊ D33
HallC3×C67 ⋊ D77
HallC7×C11 ⋊ D3×C67
HallC3×C11 ⋊ D7×C67
HallC3×C7 ⋊ D11×C67
SylowC11 ⋊ D21×C67
SylowC7 ⋊ D33×C67
SylowC3 ⋊ C67×D77

Subgroups

subgroupG/H
center, hypercenterC67D231
commutator, cosocle, hypocenterC3×C7×C11C2×C67
FrattiniC1G
Fitting, socleC3×C7×C11×C67C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C67

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15477

Conjugacy classes & character table

7839 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 24);