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C7×D1221 #30685308

order17094
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D1221
unambiguous semidirect productC3⋊(C7×D407)
unambiguous semidirect productC11⋊(C7×D111)
unambiguous semidirect productC37⋊(C7×D33)

Splittings

Fitting, socle, HallC3×C7×C11×C37 ⋊ C2
derived, HallC3×C11×C37 ⋊ C2×C7
HallC7×C11×C37 ⋊ D3
HallC3×C7×C37 ⋊ D11
HallC11×C37 ⋊ D3×C7
HallC7×C37 ⋊ D33
HallC3×C7×C11 ⋊ D37
HallC3×C37 ⋊ C7×D11
HallC7×C11 ⋊ D111
SylowC37 ⋊ C7×D33
HallC3×C11 ⋊ C7×D37
HallC3×C7 ⋊ D407
SylowC11 ⋊ C7×D111
SylowC3 ⋊ C7×D407

Subgroups

subgroupG/H
center, hypercenterC7D1221
commutator, cosocle, hypocenterC3×C11×C37C2×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C37C2
LCSG ▷ C3×C11×C37
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

4284 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D33×D37, C7×D11×D111, D3×C7×D407, …
maximal normal subgroup ofC7×D33×D37, C7×D11×D111, D3×C7×D407, …
maximal quotient ofC7×Dic1221, C2×C7×D1221

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17094, 16);