Finite Group Databasebeta

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C52×A4×C17 #19099833

order5100
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C3×C52×C17 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×A4×C17
unambiguous semidirect productC22⋊(C3×C52×C17)
unambiguous semidirect product(C22×C5)⋊(C3×C5×C17)
unambiguous semidirect product(C22×C17)⋊(C3×C52)
unambiguous semidirect product(C22×C5×C17)⋊(C3×C5)

Splittings

Fitting, socle, HallC22×C52×C17 ⋊ C3
derived, SylowC22 ⋊ C3×C52×C17
HallC22×C52 ⋊ C3×C17
HallC22×C17 ⋊ C3×C52

Subgroups

subgroupG/H
center, hypercenterC52×C17A4
commutator, hypocenterC22C3×C52×C17
FrattiniC1G
Fitting, socleC22×C52×C17C3
LCSG ▷ C22
UCSC1 ◁ C52×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×C17×C52⋊C3, C3×C52×A4×C17, C52×C7×A4×C17, …
maximal normal subgroup ofA4×C17×C52⋊C3, C3×C52×A4×C17, C52×C7×A4×C17
maximal quotient ofC52×C17×C22⋊C9, C3×C52×A4×C17, C52×C7×A4×C17, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5100, 136);