Finite Group Databasebeta

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C2×C5×C7×D5×C17 #26045466

order11900
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D5×C17
unambiguous semidirect productC5⋊(C22×C5×C7×C17)
unambiguous semidirect product(C2×C5)⋊(C2×C5×C7×C17)

Splittings

Fitting, socleC2×C52×C7×C17 ⋊ C2
derivedC5 ⋊ C22×C5×C7×C17
HallC52×C7×C17 ⋊ C22
HallC52×C17 ⋊ C22×C7
HallC52×C7 ⋊ C22×C17
SylowC52 ⋊ C22×C7×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C17D5
commutator, cosocle, hypocenterC5C22×C5×C7×C17
FrattiniC1G
Fitting, socleC2×C52×C7×C17C2
LCSG ▷ C5
UCSC1 ◁ C2×C5×C7×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4760 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C17×#3874, C2×C5×D5×C17×ΓL(1,𝔽8), C5×D3×C7×D5×C17, …
maximal normal subgroup ofC2×C5×D5×C17×ΓL(1,𝔽8), C2×C3×C5×C7×D5×C17
maximal quotient ofC5×D3×C7×D5×C17, C2×C3×C5×C7×D5×C17, C2×C5×C7×C17×D15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 115);