Finite Group Databasebeta

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C2×C52×D57 #19152903

order5700
isoclinismisoclinic class of D57
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×D57
unambiguous semidirect product(C2×C3)⋊(C52×D19)
unambiguous semidirect product(C2×C19)⋊(C52×D3)

Splittings

Fitting, socleC2×C3×C52×C19 ⋊ C2
derived, HallC3×C19 ⋊ C22×C52
HallC3×C52×C19 ⋊ C22
HallC52×C19 ⋊ C2×D3
HallC3×C52 ⋊ C2×D19
SylowC19 ⋊ C2×C52×D3
SylowC3 ⋊ C2×C52×D19

Subgroups

subgroupG/H
center, hypercenterC2×C52D57
commutator, hypocenterC3×C19C22×C52
FrattiniC1G
Fitting, socleC2×C3×C52×C19C2
LCSG ▷ C3×C19
UCSC1 ◁ C2×C52

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1500 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C52×D171, C2×C52×C3⋊(D19⋊C3), C2×C3⋊(D19⋊(C52⋊C3)), …
maximal normal subgroup ofC2×C52×C3⋊(D19⋊C3), C2×C3⋊(D19⋊(C52⋊C3)), C2×C52⋊C3×D57, …
maximal quotient ofC2×C52×D171, C52×D3×D57, C2×C52×C3⋊D57, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 160);