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C5×D1771 #31799316

order17710
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D1771
unambiguous semidirect productC7⋊(C5×D253)
unambiguous semidirect productC23⋊(C5×D77)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C2
derived, HallC7×C11×C23 ⋊ C2×C5
HallC5×C11×C23 ⋊ D7
HallC5×C7×C23 ⋊ D11
HallC5×C7×C11 ⋊ D23
HallC11×C23 ⋊ C5×D7
HallC7×C23 ⋊ C5×D11
HallC5×C23 ⋊ D77
HallC7×C11 ⋊ C5×D23
HallC5×C11 ⋊ D161
HallC5×C7 ⋊ D253
SylowC23 ⋊ C5×D77
SylowC11 ⋊ C5×D161
SylowC7 ⋊ C5×D253

Subgroups

subgroupG/H
center, hypercenterC5D1771
commutator, cosocle, hypocenterC7×C11×C23C2×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C23C2
LCSG ▷ C7×C11×C23
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

4435 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D23×D77, C5×D11×D161, C5×D7×D253, …
maximal normal subgroup ofC5×D23×D77, C5×D11×D161, C5×D7×D253, …
maximal quotient ofC5×Dic1771, C2×C5×D1771

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 10);