Finite Group Databasebeta

← Prev (#24924693) Next (#24924695) →

C5×C11×Dic49 #24924694

order10780
isoclinismisoclinic class of D49
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic49
unambiguous semidirect productC49⋊(C4×C5×C11)

Splittings

derived, SylowC49 ⋊ C4×C5×C11
HallC5×C11×C49 ⋊ C4
HallC11×C49 ⋊ C4×C5
HallC5×C49 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D49
commutator, hypocenterC49C4×C5×C11
FrattiniC2×C7C5×C11×D7
FittingC2×C5×C11×C49C2
socle, prime radicalC2×C5×C7×C11D7
cosocleC2×C49C2×C5×C11
LCSG ▷ C49
UCSC1 ◁ C2×C5×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2860 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C11×Dic49, C5×C11×Dic147, C5×C11×(C49⋊C3)⋊C4
maximal normal subgroup ofC3×C5×C11×Dic49, C5×C11×(C49⋊C3)⋊C4
maximal quotient ofC3×C5×C11×Dic49, C5×C11×Dic147

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 7);