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C3×C23⋊C8 #10587764

order552
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23⋊C8
unambiguous semidirect productC23⋊(C3×C8)

Splittings

derived, SylowC23 ⋊ C3×C8
HallC3×C23 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC3×C4D23
commutator, hypocenterC23C3×C8
FrattiniC4C3×D23
FittingC3×C4×C23C2
socle, prime radicalC2×C3×C23C4
cosocleC4×C23C2×C3
LCSG ▷ C23
UCSC1 ◁ C3×C4

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 552

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28,29,31,30,32,33,34);(4,5,7,9,11,13,15,17,19,21,23,25,26,24,22,20,18,16,14,12,10,8,6)

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C23⋊C8, D69⋊C8, #11764134, …
maximal normal subgroup ofD3×C23⋊C8, D69⋊C8, #11764134, …
maximal quotient ofC3×C23⋊C16, C2×C3×C23⋊C8, C9×C23⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(552, 2);