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C5×C7×D99 #20294126

order6930
isoclinismisoclinic class of D99
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D99
unambiguous semidirect productC9⋊(C5×C7×D11)

Splittings

Fitting, HallC5×C7×C9×C11 ⋊ C2
derived, HallC9×C11 ⋊ C2×C5×C7
HallC7×C9×C11 ⋊ C2×C5
HallC5×C9×C11 ⋊ C2×C7
HallC5×C7×C11 ⋊ D9
HallC5×C7×C9 ⋊ D11
HallC7×C11 ⋊ C5×D9
HallC7×C9 ⋊ C5×D11
HallC5×C11 ⋊ C7×D9
HallC5×C9 ⋊ C7×D11
SylowC11 ⋊ C5×C7×D9
SylowC9 ⋊ C5×C7×D11

Subgroups

subgroupG/H
center, hypercenterC5×C7D99
commutator, hypocenterC9×C11C2×C5×C7
FrattiniC3C5×C7×D33
FittingC5×C7×C9×C11C2
socleC3×C5×C7×C11D3
LCSG ▷ C9×C11
UCSC1 ◁ C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×D9×D11, C5×D7×D99, C5×D63⋊D11, …
maximal normal subgroup ofC5×C7×D9×D11, C5×D7×D99, C5×D63⋊D11, …
maximal quotient ofC5×C7×Dic99, C2×C5×C7×D99, C7×C25×D99, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 13);