Finite Group Databasebeta

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C2×C3×C5⋊D85 #19099839

order5100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3×C5⋊D85
unambiguous semidirect product(C2×C5)⋊(C3×D85)
unambiguous semidirect product(C2×C17)⋊(C3×C5⋊D5)

Splittings

Fitting, socleC2×C3×C52×C17 ⋊ C2
derived, HallC52×C17 ⋊ C22×C3
HallC3×C52×C17 ⋊ C22
HallC3×C52 ⋊ C2×D17
HallC3×C17 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×C3×D17
SylowC17 ⋊ C2×C3×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊D85
commutator, hypocenterC52×C17C22×C3
FrattiniC1G
Fitting, socleC2×C3×C52×C17C2
LCSG ▷ C52×C17
UCSC1 ◁ C2×C3

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1284 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C17⋊((C5⋊D5)⋊C9), C2×C9×C5⋊D85, C2×C3×C17⋊((C5⋊D5)⋊C3), …
maximal normal subgroup ofC2×C17⋊((C5⋊D5)⋊C9), C2×C9×C5⋊D85, C2×C3×C17⋊((C5⋊D5)⋊C3), …
maximal quotient ofC2×C9×C5⋊D85, C3×D3×C5⋊D85, C2×C3×C3⋊(C5⋊D85), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5100, 142);