Finite Group Databasebeta

← Prev (#49144707) Next (#49144709) →

C19×C23×Dic21 #49144708

order36708
automorphism?
homologyAbelianization (H1) = C4×C19×C23 · Schur multiplier (H2) = C1

Aliases

direct productC19×C23×Dic21
unambiguous semidirect productC3⋊(C19×C23×Dic7)
unambiguous semidirect productC7⋊(Dic3×C19×C23)

Splittings

derived, HallC3×C7 ⋊ C4×C19×C23
HallC3×C7×C19×C23 ⋊ C4
HallC7×C19×C23 ⋊ Dic3
HallC3×C19×C23 ⋊ Dic7
HallC3×C7×C23 ⋊ C4×C19
HallC3×C7×C19 ⋊ C4×C23
HallC7×C23 ⋊ Dic3×C19
HallC7×C19 ⋊ Dic3×C23
HallC3×C23 ⋊ C19×Dic7
HallC3×C19 ⋊ C23×Dic7
SylowC7 ⋊ Dic3×C19×C23
SylowC3 ⋊ C19×C23×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C19×C23D21
commutator, hypocenterC3×C7C4×C19×C23
FrattiniC2C19×C23×D21
Fitting, socle, prime radicalC2×C3×C7×C19×C23C2
cosocleC2×C3×C7C2×C19×C23
LCSG ▷ C3×C7
UCSC1 ◁ C2×C19×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36708

Conjugacy classes & character table

10488 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36708, 17);