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C2×C3×(C13⋊C3)⋊(C7⋊D7) #37525489

order22932
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C7

Aliases

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

Splittings

Fitting, socleC2×C3×C72×C13 ⋊ C2×C3
derived, HallC72×C13 ⋊ C22×C32
HallC3×C72×C13⋊C3 ⋊ C22
HallC2×C7⋊D91 ⋊ C32
HallC3×C13⋊C3 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×C3×D13⋊C3
SylowC13 ⋊ C2×C32×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C3(C13⋊C3)⋊(C7⋊D7)
commutator, cosocle, hypocenterC72×C13C22×C32
FrattiniC1G
Fitting, socleC2×C3×C72×C13C2×C3
LCSG ▷ C72×C13
UCSC1 ◁ C2×C3

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 3822

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

1056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 1434);