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C5×C11×D161 #31799314

order17710
isoclinismisoclinic class of D161
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D161
unambiguous semidirect productC7⋊(C5×C11×D23)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C2
derived, HallC7×C23 ⋊ C2×C5×C11
HallC7×C11×C23 ⋊ C2×C5
HallC5×C11×C23 ⋊ D7
HallC5×C7×C23 ⋊ C2×C11
HallC5×C7×C11 ⋊ D23
HallC11×C23 ⋊ C5×D7
HallC5×C23 ⋊ C11×D7
HallC7×C11 ⋊ C5×D23
HallC5×C7 ⋊ C11×D23
SylowC23 ⋊ C5×C11×D7
SylowC7 ⋊ C5×C11×D23

Subgroups

subgroupG/H
center, hypercenterC5×C11D161
commutator, cosocle, hypocenterC7×C23C2×C5×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C23C2
LCSG ▷ C7×C23
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

4510 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×D7×D23, C5×D11×D161, C5×D77⋊D23, …
maximal normal subgroup ofC5×C11×D7×D23, C5×D11×D161, C5×D77⋊D23, …
maximal quotient ofC5×C11×Dic161, C2×C5×C11×D161

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 8);