Finite Group Databasebeta

← Prev (#26046072) Next (#26046074) →

C2×C5×C7×#4294 #26046073

order11970
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C7×#4294

Splittings

derived, SylowC19 ⋊ C2×C5×C7×C9
HallC2×C5×C7×C19 ⋊ C9
HallC5×C7×C19 ⋊ C2×C9
HallC2×C7×C19 ⋊ C5×C9
HallC2×C5×C19 ⋊ C7×C9
HallC7×C19 ⋊ C2×C5×C9
HallC5×C19 ⋊ C2×C7×C9
HallC2×C19 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7C19⋊C3
commutator, hypocenterC19C2×C5×C7×C9
FrattiniC3C2×C5×C7×C19⋊C3
Fitting, socle, prime radicalC2×C3×C5×C7×C19C3
cosocleC3×C19C2×C3×C5×C7
LCSG ▷ C19
UCSC1 ◁ C2×C3×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1890 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C7×#4294, C5×C7×#4294⋊C4, C5×Dic7×#4294, …
maximal normal subgroup ofC4×C5×C7×#4294, C5×C7×#4294⋊C4, C5×Dic7×#4294, …
maximal quotient ofC4×C5×C7×#4294, C22×C5×C7×#4294

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 2);