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C2×C13×C3⋊(C3⋊(C7⋊D7)) #37525684

order22932
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2×C3×C7

Aliases

direct productC2×C13×C3⋊(C3⋊(C7⋊D7))
unambiguous semidirect product(C2×C3)⋊(C13×C3⋊(C7⋊D7))
unambiguous semidirect product(C2×C7)⋊(C13×C3⋊D21)

Splittings

Fitting, socleC2×C32×C72×C13 ⋊ C2
derived, HallC32×C72 ⋊ C22×C13
HallC32×C72×C13 ⋊ C22
HallC72×C13 ⋊ C2×C3⋊D3
HallC32×C13 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×C13×C3⋊D3
SylowC32 ⋊ C2×C13×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊(C3⋊(C7⋊D7))
commutator, cosocle, hypocenterC32×C72C22×C13
FrattiniC1G
Fitting, socleC2×C32×C72×C13C2
LCSG ▷ C32×C72
UCSC1 ◁ C2×C13

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 11466

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(17,18)(19,20)(22,23)(24,25)(26,27)(29,30)(32,33);(21,22,24,26,27,25,23)(31,32,33)(34,35);(14,15,17,19,20,18,16)(28,29,30)

Conjugacy classes & character table

5772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 1629);