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C22×#92789 #14523185

order2028
isoclinismisoclinic class of #92789
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C13

Aliases

direct productC22×#92789

Splittings

Fitting, socle, HallC22×C132 ⋊ C3
derived, SylowC132 ⋊ C22×C3

Subgroups

subgroupG/H
center, hypercenterC22#92789
commutator, cosocle, hypocenterC132C22×C3
FrattiniC1G
Fitting, socleC22×C132C3
LCSG ▷ C132
UCSC1 ◁ C22

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 156

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2)(6,7,9)(8,11,14)(10,13,12)(15,17,16)(19,20,22)(21,24,28)(23,26,25)(27,29,30);(3,4)(5,6,8,7,10,14,11,15,17,9,12,16,13)(18,19,21,22,25,24,28,30,29,20,23,27,26)

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D7⋊#92789, C2×D7×#92789, C22×C7⋊#92789, …
maximal normal subgroup ofC22×C7×#92789, C22×C11×#92789, C22×C17×#92789, …
maximal quotient ofC2×D7⋊#92789, C2×D7×#92789, C22×C7⋊#92789, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2028, 79);