Finite Group Databasebeta

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C2×C3×C5×C17×D23 #37553351

order23460
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C17×D23
unambiguous semidirect productC23⋊(C22×C3×C5×C17)
unambiguous semidirect product(C2×C23)⋊(C2×C3×C5×C17)

Splittings

Fitting, socleC2×C3×C5×C17×C23 ⋊ C2
derived, SylowC23 ⋊ C22×C3×C5×C17
HallC3×C5×C17×C23 ⋊ C22
HallC5×C17×C23 ⋊ C22×C3
HallC3×C17×C23 ⋊ C22×C5
HallC17×C23 ⋊ C22×C3×C5
HallC3×C5×C23 ⋊ C22×C17
HallC5×C23 ⋊ C22×C3×C17
HallC3×C23 ⋊ C22×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C17D23
commutator, cosocle, hypocenterC23C22×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C23C2
LCSG ▷ C23
UCSC1 ◁ C2×C3×C5×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11730

Conjugacy classes & character table

6630 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 78);