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Cayley diagram

D5×D23 #90749

order460
isoclinismisoclinic class of D5×D23
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD5×D23
unambiguous semidirect product(D5×C23)⋊C2
unambiguous semidirect product(C5×D23)⋊C2
unambiguous semidirect productD115⋊C2

Splittings

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

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C23C22
LCSG ▷ C5×C23
UCSC1

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 115

A minimal faithful permutation representation — 2 generators on 28 points:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×D23, C2×D5×D23, C3×D5×D23, …
maximal normal subgroup ofAGL(1,𝔽5)×D23, C2×D5×D23, C3×D5×D23, …
maximal quotient ofDic5×D23, D5×Dic23, #11745064, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(460, 7);