Finite Group Databasebeta

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Cayley diagram

C2×D115 #90752

order460
isoclinismisoclinic class of D115
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD230
direct productC2×D115
unambiguous semidirect product(C2×C5)⋊D23
unambiguous semidirect product(C2×C23)⋊D5

Splittings

Fitting, socleC2×C5×C23 ⋊ C2
derived, HallC5×C23 ⋊ C22
SylowC23 ⋊ C2×D5
SylowC5 ⋊ C2×D23

Subgroups

subgroupG/H
center, hypercenterC2D115
commutator, cosocle, hypocenterC5×C23C22
FrattiniC1G
Fitting, socleC2×C5×C23C2
LCSG ▷ C5×C23
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 230

A minimal faithful permutation representation — 2 generators on 30 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);(4,7)(5,6)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)

Conjugacy classes & character table

118 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745064, #11745066, #11745067, …
maximal normal subgroup of#11745064, #11745066, #11745067, …
maximal quotient ofDic230, C4×D115, D460, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(460, 10);