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C22×C5×C13⋊C3 #11715960

order780
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C13⋊C3

Splittings

Fitting, socle, HallC22×C5×C13 ⋊ C3
derived, SylowC13 ⋊ C22×C3×C5
HallC5×C13 ⋊ C22×C3
HallC22×C13 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC22×C5C13⋊C3
commutator, cosocle, hypocenterC13C22×C3×C5
FrattiniC1G
Fitting, socleC22×C5×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 260

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×Dic13⋊C3, C5×(C22⋊D13)⋊C3, C2×Dic5×C13⋊C3, …
maximal normal subgroup ofC2×C5×Dic13⋊C3, C5×(C22⋊D13)⋊C3, C2×Dic5×C13⋊C3, …
maximal quotient ofC2×C4×C5×C13⋊C3, C5×D4×C13⋊C3, C5×Q8×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(780, 43);