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C17×D273 #22604643

order9282
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D273
unambiguous semidirect productC3⋊(C17×D91)
unambiguous semidirect productC7⋊(C17×D39)
unambiguous semidirect productC13⋊(C17×D21)

Splittings

Fitting, socle, HallC3×C7×C13×C17 ⋊ C2
derived, HallC3×C7×C13 ⋊ C2×C17
HallC7×C13×C17 ⋊ D3
HallC3×C13×C17 ⋊ D7
HallC3×C7×C17 ⋊ D13
HallC13×C17 ⋊ D21
HallC7×C17 ⋊ D39
HallC7×C13 ⋊ D3×C17
HallC3×C17 ⋊ D91
HallC3×C13 ⋊ D7×C17
HallC3×C7 ⋊ C17×D13
SylowC13 ⋊ C17×D21
SylowC7 ⋊ C17×D39
SylowC3 ⋊ C17×D91

Subgroups

subgroupG/H
center, hypercenterC17D273
commutator, hypocenterC3×C7×C13C2×C17
FrattiniC1G
Fitting, socleC3×C7×C13×C17C2
LCSG ▷ C3×C7×C13
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2346 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD17×D273, C17×D13×D21, D221⋊D21, …
maximal normal subgroup ofD17×D273, C17×D13×D21, D221⋊D21, …
maximal quotient ofC17×Dic273, C2×C17×D273, C17×D819, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 19);