Finite Group Databasebeta

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C2×C5×D5×C79⋊C3 #37557222

order23700
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D5×C79⋊C3
unambiguous semidirect productC5⋊(C22×C5×C79⋊C3)
unambiguous semidirect product(C2×C5)⋊(C2×C5×C79⋊C3)
unambiguous semidirect product(C2×D5×C79)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D5×C79)⋊C3

Splittings

Fitting, socleC2×C52×C79 ⋊ C2×C3
derivedC5×C79 ⋊ C22×C3×C5
HallC2×C5×D5×C79 ⋊ C3
HallC52×C79⋊C3 ⋊ C22
HallC52×C79 ⋊ C22×C3
SylowC79 ⋊ C2×C3×C5×D5
SylowC52 ⋊ C22×C79⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5D5×C79⋊C3
commutator, cosocle, hypocenterC5×C79C22×C3×C5
FrattiniC1G
Fitting, socleC2×C52×C79C2×C3
LCSG ▷ C5×C79
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1580

Conjugacy classes & character table

1160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23700, 105);