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Cayley diagram

C2×C23⋊C11 #92780

order506
isoclinismisoclinic class of C23⋊C11
automorphismAut(G) = AGL(1,𝔽23) (order 506) · Inn(G) = C23⋊C11 · Out(G) = C2
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C23⋊C11
unambiguous semidirect product(C2×C23)⋊C11

Splittings

Fitting, socle, HallC2×C23 ⋊ C11
derived, SylowC23 ⋊ C2×C11

Subgroups

subgroupG/H
center, hypercenterC2C23⋊C11
commutator, cosocle, hypocenterC23C2×C11
FrattiniC1G
Fitting, socleC2×C23C11
LCSG ▷ C23
UCSC1 ◁ C2

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 46

A minimal faithful permutation representation — 2 generators on 25 points:

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

Conjugacy classes & character table

26 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic23⋊C11, C4×C23⋊C11, C2×AGL(1,𝔽23), …
maximal normal subgroup ofDic23⋊C11, C4×C23⋊C11, C2×AGL(1,𝔽23), …
maximal quotient ofC4×C23⋊C11, C22×C23⋊C11, D3×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(506, 2);