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C7×D2211 #44526240

order30954
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2211
unambiguous semidirect productC3⋊(C7×D737)
unambiguous semidirect productC11⋊(C7×D201)
unambiguous semidirect productC67⋊(C7×D33)

Splittings

Fitting, socle, HallC3×C7×C11×C67 ⋊ C2
derived, HallC3×C11×C67 ⋊ C2×C7
HallC7×C11×C67 ⋊ D3
HallC3×C7×C67 ⋊ D11
HallC11×C67 ⋊ D3×C7
HallC7×C67 ⋊ D33
HallC3×C7×C11 ⋊ D67
HallC3×C67 ⋊ C7×D11
HallC7×C11 ⋊ D201
SylowC67 ⋊ C7×D33
HallC3×C11 ⋊ C7×D67
HallC3×C7 ⋊ D737
SylowC11 ⋊ C7×D201
SylowC3 ⋊ C7×D737

Subgroups

subgroupG/H
center, hypercenterC7D2211
commutator, cosocle, hypocenterC3×C11×C67C2×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C67C2
LCSG ▷ C3×C11×C67
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15477

Conjugacy classes & character table

7749 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 21);