Finite Group Databasebeta

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C2×C7×C3⋊((C11⋊D11)⋊C3) #44479157

order30492
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C7×C3⋊((C11⋊D11)⋊C3)
unambiguous semidirect product(C2×C3)⋊(C7×(C11⋊D11)⋊C3)
unambiguous semidirect product(C2×C3⋊(C11⋊D11))⋊(C3×C7)

Splittings

Fitting, socleC2×C3×C7×C112 ⋊ C2×C3
derivedC3×C112 ⋊ C22×C3×C7
HallC3×C7×C112⋊C3 ⋊ C22
HallC3×C112⋊C3 ⋊ C22×C7
HallC7×C112 ⋊ C2×C3×D3
SylowC112 ⋊ C2×C3×D3×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊((C11⋊D11)⋊C3)
commutator, cosocle, hypocenterC3×C112C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C112C2×C3
LCSG ▷ C3×C112
UCSC1 ◁ C2×C7

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 1386

A minimal faithful permutation representation — 2 generators on 45 points:

(4,5)(6,7,8,9,10,11,12)(13,14,16)(15,27,29,19,20,36)(17,35,32,24,25,42)(18,23,33,28,22,34)(21,39,41,30,31,45)(26,40,44,37,38,43);(1,2)(3,4,5)(13,15,21,32,34,43,44,33,42,30,19)(14,17,26,39,20,28,18,27,31,37,24)(16,22,25,36,38,41,45,40,29,35,23)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 380);