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C7×C9×Dic5 #11929454

order1260
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×Dic5

Splittings

derived, SylowC5 ⋊ C4×C7×C9
HallC5×C7×C9 ⋊ C4
HallC5×C9 ⋊ C4×C7
HallC5×C7 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9D5
commutator, hypocenterC5C4×C7×C9
FrattiniC2×C3C3×C7×D5
FittingC2×C5×C7×C9C2
socle, prime radicalC2×C3×C5×C7C2×C3
cosocleC2×C3×C5C2×C3×C7
LCSG ▷ C5
UCSC1 ◁ C2×C7×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);(17,19,18,20)(22,25)(23,24)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×C9×C11×Dic5, C7×C9×Dic55, C7×C9×C13×Dic5, …
maximal normal subgroup ofC7×C9×C11×Dic5, C7×C9×C13×Dic5, C7×C9×C17×Dic5, …
maximal quotient ofC7×C9×C11×Dic5, C7×C9×Dic55, C7×C9×C13×Dic5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 6);