Finite Group Databasebeta

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C7×C11×C22⋊C9 #14583870

order2772
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C7×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC7×C11×C22⋊C9
unambiguous semidirect productC22⋊(C7×C9×C11)
unambiguous semidirect product(C22×C11)⋊(C7×C9)

Splittings

derived, SylowC22 ⋊ C7×C9×C11
HallC22×C7×C11 ⋊ C9
HallC22×C11 ⋊ C7×C9
HallC22×C7 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11A4
commutator, hypocenterC22C7×C9×C11
FrattiniC3C7×C11×A4
Fitting, socle, prime radicalC22×C3×C7×C11C3
cosocleC22×C3C3×C7×C11
LCSG ▷ C22
UCSC1 ◁ C3×C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 1386

A minimal faithful permutation representation — 2 generators on 31 points:

(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18)(20,21,22)(23,24,26,25,27,29,28,30,31);(19,22)(20,21)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×C22⋊C9×C11⋊C5, C5×C7×C11×C22⋊C9, C11×C22⋊C9×C49, …
maximal normal subgroup ofC7×C22⋊C9×C11⋊C5, C5×C7×C11×C22⋊C9, C11×C22⋊C9×C49, …
maximal quotient ofC5×C7×C11×C22⋊C9, C11×C22⋊C9×C49, C72×C11×C22⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2772, 26);