Finite Group Databasebeta

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C3×C7×C5⋊D115 #37563407

order24150
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C5

Aliases

direct productC3×C7×C5⋊D115
unambiguous semidirect productC5⋊(C3×C7×D115)
unambiguous semidirect productC23⋊(C3×C7×C5⋊D5)

Splittings

Fitting, socle, HallC3×C52×C7×C23 ⋊ C2
derived, HallC52×C23 ⋊ C2×C3×C7
HallC52×C7×C23 ⋊ C2×C3
HallC3×C52×C23 ⋊ C2×C7
HallC3×C52×C7 ⋊ D23
HallC3×C7×C23 ⋊ C5⋊D5
HallC52×C7 ⋊ C3×D23
HallC7×C23 ⋊ C3×C5⋊D5
HallC3×C52 ⋊ C7×D23
HallC3×C23 ⋊ C7×C5⋊D5
SylowC52 ⋊ C3×C7×D23
SylowC23 ⋊ C3×C7×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC3×C7C5⋊D115
commutator, cosocle, hypocenterC52×C23C2×C3×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C23C2
LCSG ▷ C52×C23
UCSC1 ◁ C3×C7

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12075

Conjugacy classes & character table

6069 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24150, 66);