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C2×C3⋊(C5⋊D95) #19152907

order5700
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3⋊(C5⋊D95)
unambiguous semidirect product(C2×C3)⋊(C5⋊D95)
unambiguous semidirect product(C2×C5)⋊D285
unambiguous semidirect product(C2×C19)⋊(C3⋊(C5⋊D5))

Splittings

Fitting, socleC2×C3×C52×C19 ⋊ C2
derived, HallC3×C52×C19 ⋊ C22
HallC52×C19 ⋊ C2×D3
HallC3×C52 ⋊ C2×D19
HallC3×C19 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×D57
SylowC19 ⋊ C2×C3⋊(C5⋊D5)
SylowC3 ⋊ C2×C5⋊D95

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊D95)
commutator, hypocenterC3×C52×C19C22
FrattiniC1G
Fitting, socleC2×C3×C52×C19C2
LCSG ▷ C3×C52×C19
UCSC1 ◁ C2

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1428 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊D855, C2×C3⋊(C5⋊(C5⋊(D19⋊C3))), C2×C3⋊#15668133, …
maximal normal subgroup ofC2×C3⋊(C5⋊(C5⋊(D19⋊C3))), C2×C3⋊#15668133, C2×C3⋊#15668135, …
maximal quotient ofC2×C5⋊D855, D3×C3⋊(C5⋊D95), C2×C3⋊(C3⋊(C5⋊D95)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5700, 164);