Finite Group Databasebeta

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C17×C23×Dic21 #45659249

order32844
automorphism?
homologyAbelianization (H1) = C4×C17×C23 · Schur multiplier (H2) = C1

Aliases

direct productC17×C23×Dic21
unambiguous semidirect productC3⋊(C17×C23×Dic7)
unambiguous semidirect productC7⋊(Dic3×C17×C23)

Splittings

derived, HallC3×C7 ⋊ C4×C17×C23
HallC3×C7×C17×C23 ⋊ C4
HallC7×C17×C23 ⋊ Dic3
HallC3×C17×C23 ⋊ Dic7
HallC3×C7×C23 ⋊ C4×C17
HallC3×C7×C17 ⋊ C4×C23
HallC7×C23 ⋊ Dic3×C17
HallC7×C17 ⋊ Dic3×C23
HallC3×C23 ⋊ C17×Dic7
HallC3×C17 ⋊ C23×Dic7
SylowC7 ⋊ Dic3×C17×C23
SylowC3 ⋊ C17×C23×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C17×C23D21
commutator, hypocenterC3×C7C4×C17×C23
FrattiniC2C17×C23×D21
Fitting, socle, prime radicalC2×C3×C7×C17×C23C2
cosocleC2×C3×C7C2×C17×C23
LCSG ▷ C3×C7
UCSC1 ◁ C2×C17×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32844

Conjugacy classes & character table

9384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 14);