Finite Group Databasebeta

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C2×C5×D935 #34035273

order18700
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D935
unambiguous semidirect product(C2×C5)⋊(C5×D187)
unambiguous semidirect product(C2×C17)⋊(C5×D55)

Splittings

Fitting, socleC2×C52×C11×C17 ⋊ C2
derivedC5×C11×C17 ⋊ C22×C5
HallC52×C11×C17 ⋊ C22
HallC52×C17 ⋊ C2×D11
HallC52×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×C5×D5
SylowC52 ⋊ C2×D187
SylowC17 ⋊ C2×C5×D55
SylowC11 ⋊ C2×C5×D85

Subgroups

subgroupG/H
center, hypercenterC2×C5D935
commutator, cosocle, hypocenterC5×C11×C17C22×C5
FrattiniC1G
Fitting, socleC2×C52×C11×C17C2
LCSG ▷ C5×C11×C17
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3740

Conjugacy classes & character table

4690 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 158);