Finite Group Databasebeta

← Prev (#11929452) Next (#11929454) →

C5×C9×Dic7 #11929453

order1260
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×Dic7

Splittings

derived, SylowC7 ⋊ C4×C5×C9
HallC5×C7×C9 ⋊ C4
HallC7×C9 ⋊ C4×C5
HallC5×C7 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D7
commutator, hypocenterC7C4×C5×C9
FrattiniC2×C3C3×C5×D7
FittingC2×C5×C7×C9C2
socle, prime radicalC2×C3×C5×C7C2×C3
cosocleC2×C3×C7C2×C3×C5
LCSG ▷ C7
UCSC1 ◁ C2×C5×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 1260

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14)(15,16)(17,18)(19,20,21,22,23,24,25);(15,17,16,18)(20,25)(21,24)(22,23)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C9×C11×Dic7, C5×C9×Dic77, C9×Dic7×C11⋊C5, …
maximal normal subgroup ofC5×C9×C11×Dic7, C5×C9×C13×Dic7, C5×C9×C17×Dic7, …
maximal quotient ofC5×C9×C11×Dic7, C5×C9×Dic77, C9×Dic7×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 5);