Finite Group Databasebeta

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C5×Dic3×C17×C23 #37553282

order23460
automorphism?
homologyAbelianization (H1) = C4×C5×C17×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×C17×C23
unambiguous semidirect productC3⋊(C4×C5×C17×C23)

Splittings

derived, SylowC3 ⋊ C4×C5×C17×C23
HallC3×C5×C17×C23 ⋊ C4
HallC3×C17×C23 ⋊ C4×C5
HallC3×C5×C23 ⋊ C4×C17
HallC3×C5×C17 ⋊ C4×C23
HallC3×C23 ⋊ C4×C5×C17
HallC3×C17 ⋊ C4×C5×C23
HallC3×C5 ⋊ C4×C17×C23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17×C23D3
commutator, hypocenterC3C4×C5×C17×C23
FrattiniC2C5×D3×C17×C23
Fitting, socle, prime radicalC2×C3×C5×C17×C23C2
cosocleC2×C3C2×C5×C17×C23
LCSG ▷ C3
UCSC1 ◁ C2×C5×C17×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23460

Conjugacy classes & character table

11730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 9);