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C5×C11×D7×C23 #31799313

order17710
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D7×C23
unambiguous semidirect productC7⋊(C2×C5×C11×C23)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C2
derived, SylowC7 ⋊ C2×C5×C11×C23
HallC7×C11×C23 ⋊ C2×C5
HallC5×C7×C23 ⋊ C2×C11
HallC5×C7×C11 ⋊ C2×C23
HallC7×C23 ⋊ C2×C5×C11
HallC7×C11 ⋊ C2×C5×C23
HallC5×C7 ⋊ C2×C11×C23

Subgroups

subgroupG/H
center, hypercenterC5×C11×C23D7
commutator, cosocle, hypocenterC7C2×C5×C11×C23
FrattiniC1G
Fitting, socleC5×C7×C11×C23C2
LCSG ▷ C7
UCSC1 ◁ C5×C11×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

6325 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×D7×D23, C5×D7×D11×C23, C5×D7×D253, …
maximal normal subgroup ofC5×C11×D7×D23, C5×D7×D11×C23, C5×D7×D253, …
maximal quotient ofC5×C11×C23×Dic7, C2×C5×C11×D7×C23

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 7);