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C22⋊A4×C9⋊C9 #72229230

order3888
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C24×C33

Aliases

direct productC22⋊A4×C9⋊C9

Splittings

FittingC24×C9⋊C9 ⋊ C3
SylowC24 ⋊ C3×C9⋊C9

Subgroups

subgroupG/H
center, FrattiniC32C32×C22⋊A4
commutatorC24×C3C32×C9
FittingC24×C9⋊C9C3
socle, cosocleC24×C32C33
prime radicalC32×C22⋊A4C32
hypercenterC9⋊C9C22⋊A4
hypocenterC24C3×C9⋊C9
LCSG ▷ C24×C3 ▷ C24
UCSC1 ◁ C32 ◁ C9⋊C9

970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 972

A minimal faithful permutation representation — 3 generators on 26 points:

(10,11,14,12,13,17,15,16,18)(23,26)(24,25);(20,22,21)(24,26,25);(1,2,4,3,5,7,6,8,9)(11,13,16)(14,18,17)(19,22)(20,21)

Conjugacy classes & character table

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

Relationships

maximal subgroup of#72229286, #72229393, C2×C22⋊A4×C9⋊C9
maximal normal subgroup of#72229286, #72229393, C2×C22⋊A4×C9⋊C9
maximal quotient ofC2×C22⋊A4×C9⋊C9, C9⋊C9×#997

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((10,11,14,12,13,17,15,16,18)(23,26)(24,25), (20,22,21)(24,26,25), (1,2,4,3,5,7,6,8,9)(11,13,16)(14,18,17)(19,22)(20,21));