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C3×(C5⋊D5)⋊D19 #19152863

order5700
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×(C5⋊D5)⋊D19

Splittings

Fitting, socle, HallC3×C52×C19 ⋊ C22
derived, HallC52×C19 ⋊ C22×C3
HallC3×C52 ⋊ C2×D19
HallC3×C19 ⋊ D52
SylowC52 ⋊ C2×C3×D19
SylowC19 ⋊ C3×D52

Subgroups

subgroupG/H
center, hypercenterC3(C5⋊D5)⋊D19
commutator, hypocenterC52×C19C22×C3
FrattiniC1G
Fitting, socleC3×C52×C19C22
LCSG ▷ C52×C19
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

426 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C5⋊(#4294⋊C2))⋊D5, C9×(C5⋊D5)⋊D19, C3×(C5⋊(D19⋊C3))⋊D5, …
maximal normal subgroup of(C5⋊(#4294⋊C2))⋊D5, C9×(C5⋊D5)⋊D19, C3×(C5⋊(D19⋊C3))⋊D5, …
maximal quotient ofC9×(C5⋊D5)⋊D19, C32×(C5⋊D5)⋊D19, C3×D95⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 120);