Finite Group Databasebeta

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C17×C23×Dic15 #37553286

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

Aliases

direct productC17×C23×Dic15
unambiguous semidirect productC3⋊(C17×Dic5×C23)

Splittings

derived, HallC3×C5 ⋊ C4×C17×C23
HallC3×C5×C17×C23 ⋊ C4
HallC5×C17×C23 ⋊ Dic3
HallC3×C17×C23 ⋊ Dic5
HallC3×C5×C23 ⋊ C4×C17
HallC3×C5×C17 ⋊ C4×C23
HallC5×C23 ⋊ Dic3×C17
HallC5×C17 ⋊ Dic3×C23
HallC3×C23 ⋊ C17×Dic5
HallC3×C17 ⋊ Dic5×C23
SylowC5 ⋊ Dic3×C17×C23
SylowC3 ⋊ C17×Dic5×C23

Subgroups

subgroupG/H
center, hypercenterC2×C17×C23D15
commutator, hypocenterC3×C5C4×C17×C23
FrattiniC2C17×C23×D15
Fitting, socle, prime radicalC2×C3×C5×C17×C23C2
cosocleC2×C3×C5C2×C17×C23
LCSG ▷ C3×C5
UCSC1 ◁ C2×C17×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23460

Conjugacy classes & character table

7038 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 13);