Finite Group Databasebeta

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C3×C19×Dic77 #31798196

order17556
isoclinismisoclinic class of D77
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19×Dic77
unambiguous semidirect productC11⋊(C3×C19×Dic7)

Splittings

derived, HallC7×C11 ⋊ C3×C4×C19
HallC3×C7×C11×C19 ⋊ C4
HallC7×C11×C19 ⋊ C3×C4
HallC3×C11×C19 ⋊ Dic7
HallC3×C7×C19 ⋊ Dic11
HallC3×C7×C11 ⋊ C4×C19
HallC11×C19 ⋊ C3×Dic7
HallC7×C19 ⋊ C3×Dic11
HallC3×C11 ⋊ C19×Dic7
HallC3×C7 ⋊ C19×Dic11
SylowC11 ⋊ C3×C19×Dic7
SylowC7 ⋊ C3×C19×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C19D77
commutator, hypocenterC7×C11C3×C4×C19
FrattiniC2C3×C19×D77
Fitting, socle, prime radicalC2×C3×C7×C11×C19C2
cosocleC2×C7×C11C2×C3×C19
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17556

Conjugacy classes & character table

4560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 11);