Finite Group Databasebeta

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C9×#3068 #11767789

order1152
nilpotency class3
isoclinismisoclinic class of #3068
automorphism?
homologyAbelianization (H1) = C24×C9 · Schur multiplier (H2) = C25

Aliases

direct productC9×#3068

Subgroups

subgroupG/H
centerC2×C9C2×#121
commutatorC2×C4C24×C9
Frattini, cosocleC2×C3×C4C24×C3
socleC2×C3C2×C3×#121
prime radicalC3×#3068C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C9 ◁ C22×C4×C9 ◁ G

699 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 144

A minimal faithful permutation representation — 4 generators on 25 points:

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

Conjugacy classes & character table

261 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD9×#3068, #72268983
maximal subgroup ofD9×#3068, C9×#61110, #72268983
maximal normal subgroup ofD9×#3068, C9×#61110, #72268983

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 1800);