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C2×D7579 #44476374

order30316
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD15158
direct productC2×D7579
unambiguous semidirect product(C2×C11)⋊D689
unambiguous semidirect product(C2×C13)⋊D583
unambiguous semidirect product(C2×C53)⋊D143

Splittings

Fitting, socleC2×C11×C13×C53 ⋊ C2
derived, HallC11×C13×C53 ⋊ C22
HallC13×C53 ⋊ C2×D11
HallC11×C53 ⋊ C2×D13
HallC11×C13 ⋊ C2×D53
SylowC53 ⋊ C2×D143
SylowC13 ⋊ C2×D583
SylowC11 ⋊ C2×D689

Subgroups

subgroupG/H
center, hypercenterC2D7579
commutator, cosocle, hypocenterC11×C13×C53C22
FrattiniC1G
Fitting, socleC2×C11×C13×C53C2
LCSG ▷ C11×C13×C53
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 79
transitive degreeμt(G) = 15158

A minimal faithful permutation representation — 2 generators on 79 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79);(4,13)(5,12)(6,11)(7,10)(8,9)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)(28,79)(29,78)(30,77)(31,76)(32,75)(33,74)(34,73)(35,72)(36,71)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,64)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)

Conjugacy classes & character table

7582 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD30316
maximal normal subgroup ofD30316
maximal quotient ofDic15158, D30316

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30316, 46);