Finite Group Databasebeta

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C2×C5×D1235 #37590870

order24700
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1235
unambiguous semidirect product(C2×C5)⋊(C5×D247)
unambiguous semidirect product(C2×C13)⋊(C5×D95)
unambiguous semidirect product(C2×C19)⋊(C5×D65)

Splittings

Fitting, socleC2×C52×C13×C19 ⋊ C2
derivedC5×C13×C19 ⋊ C22×C5
HallC52×C13×C19 ⋊ C22
HallC52×C19 ⋊ C2×D13
HallC52×C13 ⋊ C2×D19
HallC13×C19 ⋊ C2×C5×D5
SylowC52 ⋊ C2×D247
SylowC19 ⋊ C2×C5×D65
SylowC13 ⋊ C2×C5×D95

Subgroups

subgroupG/H
center, hypercenterC2×C5D1235
commutator, cosocle, hypocenterC5×C13×C19C22×C5
FrattiniC1G
Fitting, socleC2×C52×C13×C19C2
LCSG ▷ C5×C13×C19
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4940

Conjugacy classes & character table

6190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24700, 114);