Finite Group Databasebeta

← Prev (#37613431) Next (#37613433) →

C2×C3×C7×D295 #37613432

order24780
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D295
unambiguous semidirect product(C2×C5)⋊(C3×C7×D59)
unambiguous semidirect product(C2×C59)⋊(C3×C7×D5)

Splittings

Fitting, socleC2×C3×C5×C7×C59 ⋊ C2
derived, HallC5×C59 ⋊ C22×C3×C7
HallC3×C5×C7×C59 ⋊ C22
HallC5×C7×C59 ⋊ C22×C3
HallC3×C7×C59 ⋊ C2×D5
HallC3×C5×C59 ⋊ C22×C7
HallC7×C59 ⋊ C2×C3×D5
HallC3×C59 ⋊ C2×C7×D5
HallC3×C5×C7 ⋊ C2×D59
SylowC59 ⋊ C2×C3×C7×D5
HallC5×C7 ⋊ C2×C3×D59
HallC3×C5 ⋊ C2×C7×D59
SylowC5 ⋊ C2×C3×C7×D59

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D295
commutator, cosocle, hypocenterC5×C59C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C59C2
LCSG ▷ C5×C59
UCSC1 ◁ C2×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12390

Conjugacy classes & character table

6258 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 94);