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C11×C23×D35 #31799321

order17710
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C2×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC11×C23×D35
unambiguous semidirect productC5⋊(C11×D7×C23)
unambiguous semidirect productC7⋊(D5×C11×C23)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C2
derived, HallC5×C7 ⋊ C2×C11×C23
HallC7×C11×C23 ⋊ D5
HallC5×C11×C23 ⋊ D7
HallC5×C7×C23 ⋊ C2×C11
HallC5×C7×C11 ⋊ C2×C23
HallC7×C23 ⋊ D5×C11
HallC5×C23 ⋊ C11×D7
HallC7×C11 ⋊ D5×C23
HallC5×C11 ⋊ D7×C23
SylowC7 ⋊ D5×C11×C23
SylowC5 ⋊ C11×D7×C23

Subgroups

subgroupG/H
center, hypercenterC11×C23D35
commutator, cosocle, hypocenterC5×C7C2×C11×C23
FrattiniC1G
Fitting, socleC5×C7×C11×C23C2
LCSG ▷ C5×C7
UCSC1 ◁ C11×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

4807 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D23×D35, D11×C23×D35, D35×D253, …
maximal normal subgroup ofC11×D23×D35, D11×C23×D35, D35×D253, …
maximal quotient ofC11×C23×Dic35, C2×C11×C23×D35

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 15);