Finite Group Databasebeta

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C2×C17×C3⋊(C3⋊(C7⋊D7)) #44473024

order29988
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2×C3×C7

Aliases

direct productC2×C17×C3⋊(C3⋊(C7⋊D7))
unambiguous semidirect product(C2×C3)⋊(C17×C3⋊(C7⋊D7))
unambiguous semidirect product(C2×C7)⋊(C17×C3⋊D21)

Splittings

Fitting, socleC2×C32×C72×C17 ⋊ C2
derived, HallC32×C72 ⋊ C22×C17
HallC32×C72×C17 ⋊ C22
HallC72×C17 ⋊ C2×C3⋊D3
HallC32×C17 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×C17×C3⋊D3
SylowC32 ⋊ C2×C17×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊(C3⋊(C7⋊D7))
commutator, cosocle, hypocenterC32×C72C22×C17
FrattiniC1G
Fitting, socleC2×C32×C72×C17C2
LCSG ▷ C32×C72
UCSC1 ◁ C2×C17

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 14994

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

7548 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 665);