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C23⋊#261 #11924768

order1196
isoclinismisoclinic class of C23⋊#261
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC23⋊#261

Splittings

Fitting, socle, derived, HallC13×C23 ⋊ C4
SylowC23 ⋊ #261
SylowC13 ⋊ Dic23

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C23C4
prime radical, cosocleC23×D13C2
LCSG ▷ C13×C23
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 299

Polycyclic presentation:

2^2,13,23|a^2=b,c^a=c^8,d^a=d^22,c^b=c^12

Conjugacy classes & character table

95 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23⋊AGL(1,𝔽13), C3×C23⋊#261, C3⋊(C23⋊#261), …
maximal normal subgroup ofC23⋊AGL(1,𝔽13), C3×C23⋊#261, (C23⋊C11)⋊#261, …
maximal quotient ofC3×C23⋊#261, C3⋊(C23⋊#261), C11×C23⋊#261, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1196, 6);