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C23×D385 #31799323

order17710
automorphism?
homologyAbelianization (H1) = C2×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×D385
unambiguous semidirect productC5⋊(C23×D77)
unambiguous semidirect productC7⋊(C23×D55)
unambiguous semidirect productC11⋊(C23×D35)

Splittings

Fitting, socle, HallC5×C7×C11×C23 ⋊ C2
derived, HallC5×C7×C11 ⋊ C2×C23
HallC7×C11×C23 ⋊ D5
HallC5×C11×C23 ⋊ D7
HallC5×C7×C23 ⋊ D11
HallC11×C23 ⋊ D35
HallC7×C23 ⋊ D55
HallC5×C23 ⋊ D77
HallC7×C11 ⋊ D5×C23
HallC5×C11 ⋊ D7×C23
HallC5×C7 ⋊ D11×C23
SylowC11 ⋊ C23×D35
SylowC7 ⋊ C23×D55
SylowC5 ⋊ C23×D77

Subgroups

subgroupG/H
center, hypercenterC23D385
commutator, cosocle, hypocenterC5×C7×C11C2×C23
FrattiniC1G
Fitting, socleC5×C7×C11×C23C2
LCSG ▷ C5×C7×C11
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8855

Conjugacy classes & character table

4462 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23×D385, D11×C23×D35, D253⋊D35, …
maximal normal subgroup ofD23×D385, D11×C23×D35, D253⋊D35, …
maximal quotient ofC23×Dic385, C2×C23×D385

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 17);