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C2×C5×C3⋊D87 #19104894

order5220
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C3⋊D87
unambiguous semidirect product(C2×C3)⋊(C5×D87)
unambiguous semidirect product(C2×C29)⋊(C5×C3⋊D3)

Splittings

Fitting, socleC2×C32×C5×C29 ⋊ C2
derived, HallC32×C29 ⋊ C22×C5
HallC32×C5×C29 ⋊ C22
HallC5×C29 ⋊ C2×C3⋊D3
HallC32×C5 ⋊ C2×D29
SylowC29 ⋊ C2×C5×C3⋊D3
SylowC32 ⋊ C2×C5×D29

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D87
commutator, hypocenterC32×C29C22×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C29C2
LCSG ▷ C32×C29
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C25×C3⋊D87, C5×D5×C3⋊D87, C2×C52×C3⋊D87, …
maximal normal subgroup ofC2×C25×C3⋊D87, C2×C52×C3⋊D87, C2×C5×C3⋊(C3⋊(D29⋊C7)), …
maximal quotient ofC2×C25×C3⋊D87, C5×D5×C3⋊D87, C2×C52×C3⋊D87, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5220, 104);