Finite Group Databasebeta

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C7×D627 #22578614

order8778
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D627
unambiguous semidirect productC3⋊(C7×D209)
unambiguous semidirect productC11⋊(C7×D57)
unambiguous semidirect productC19⋊(C7×D33)

Splittings

Fitting, socle, HallC3×C7×C11×C19 ⋊ C2
derived, HallC3×C11×C19 ⋊ C2×C7
HallC7×C11×C19 ⋊ D3
HallC3×C7×C19 ⋊ D11
HallC3×C7×C11 ⋊ D19
HallC11×C19 ⋊ D3×C7
HallC7×C19 ⋊ D33
HallC7×C11 ⋊ D57
HallC3×C19 ⋊ C7×D11
HallC3×C11 ⋊ C7×D19
HallC3×C7 ⋊ D209
SylowC19 ⋊ C7×D33
SylowC11 ⋊ C7×D57
SylowC3 ⋊ C7×D209

Subgroups

subgroupG/H
center, hypercenterC7D627
commutator, hypocenterC3×C11×C19C2×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C19C2
LCSG ▷ C3×C11×C19
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2205 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D19×D33, C7×D11×D57, D3×C7×D209, …
maximal normal subgroup ofC7×D19×D33, C7×D11×D57, D3×C7×D209, …
maximal quotient ofC7×Dic627, C2×C7×D627, C7×D1881, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 16);