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C3×C5×D273 #22551298

order8190
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D273
unambiguous semidirect productC3⋊(C3×C5×D91)

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C2
derivedC3×C7×C13 ⋊ C2×C3×C5
HallC32×C7×C13 ⋊ C2×C5
HallC32×C5×C13 ⋊ D7
HallC5×C7×C13 ⋊ C3×D3
HallC32×C5×C7 ⋊ D13
HallC32×C13 ⋊ C5×D7
HallC7×C13 ⋊ C3×C5×D3
HallC5×C13 ⋊ C3×D21
HallC32×C7 ⋊ C5×D13
HallC32×C5 ⋊ D91
HallC5×C7 ⋊ C3×D39
SylowC13 ⋊ C3×C5×D21
SylowC32 ⋊ C5×D91
SylowC7 ⋊ C3×C5×D39

Subgroups

subgroupG/H
center, hypercenterC3×C5D273
commutator, hypocenterC3×C7×C13C2×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C13C2
LCSG ▷ C3×C7×C13
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2070 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D13×D21, C3×C5×D7×D39, C3×C5×D3×D91, …
maximal normal subgroup ofC3×C5×D13×D21, C3×C5×D7×D39, C3×C5×D3×D91, …
maximal quotient ofC3×C5×Dic273, C2×C3×C5×D273

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 132);