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C22×#92788 #14523184

order2028
isoclinismisoclinic class of #92788
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC22×#92788

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC22#92788
commutator, cosocle, hypocenterC132C22×C3
FrattiniC1G
Fitting, socleC22×C132C3
LCSG ▷ C132
UCSC1 ◁ C22

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 676

A minimal faithful permutation representation — 3 generators on 30 points:

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

Conjugacy classes & character table

236 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×#92788⋊C7, C2×#20296910, C2×#20296911, …
maximal normal subgroup ofC22×#92788⋊C7, C22×C7×#92788, C22×C11×#92788, …
maximal quotient ofC2×#20296910, C2×#20296911, C2×D7×#92788, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2028, 78);