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C17×D805 #41032850

order27370
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D805
unambiguous semidirect productC5⋊(C17×D161)
unambiguous semidirect productC7⋊(C17×D115)
unambiguous semidirect productC23⋊(C17×D35)

Splittings

Fitting, socle, HallC5×C7×C17×C23 ⋊ C2
derived, HallC5×C7×C23 ⋊ C2×C17
HallC7×C17×C23 ⋊ D5
HallC5×C17×C23 ⋊ D7
HallC5×C7×C17 ⋊ D23
HallC17×C23 ⋊ D35
HallC7×C23 ⋊ D5×C17
HallC7×C17 ⋊ D115
HallC5×C23 ⋊ D7×C17
HallC5×C17 ⋊ D161
HallC5×C7 ⋊ C17×D23
SylowC23 ⋊ C17×D35
SylowC7 ⋊ C17×D115
SylowC5 ⋊ C17×D161

Subgroups

subgroupG/H
center, hypercenterC17D805
commutator, cosocle, hypocenterC5×C7×C23C2×C17
FrattiniC1G
Fitting, socleC5×C7×C17×C23C2
LCSG ▷ C5×C7×C23
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13685

Conjugacy classes & character table

6868 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27370, 14);