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C5×D693 #20294128

order6930
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D693
unambiguous semidirect productC7⋊(C5×D99)
unambiguous semidirect productC9⋊(C5×D77)

Splittings

Fitting, HallC5×C7×C9×C11 ⋊ C2
derived, HallC7×C9×C11 ⋊ C2×C5
HallC5×C9×C11 ⋊ D7
HallC5×C7×C11 ⋊ D9
HallC5×C7×C9 ⋊ D11
HallC9×C11 ⋊ C5×D7
HallC7×C11 ⋊ C5×D9
HallC7×C9 ⋊ C5×D11
HallC5×C11 ⋊ D63
HallC5×C9 ⋊ D77
HallC5×C7 ⋊ D99
SylowC11 ⋊ C5×D63
SylowC9 ⋊ C5×D77
SylowC7 ⋊ C5×D99

Subgroups

subgroupG/H
center, hypercenterC5D693
commutator, hypocenterC7×C9×C11C2×C5
FrattiniC3C5×D231
FittingC5×C7×C9×C11C2
socleC3×C5×C7×C11D3
LCSG ▷ C7×C9×C11
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D11×D63, C5×D7×D99, C5×D9×D77, …
maximal normal subgroup ofC5×D11×D63, C5×D7×D99, C5×D9×D77, …
maximal quotient ofC5×Dic693, C2×C5×D693, C25×D693, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 15);