Finite Group Databasebeta

← Prev (#63284) Next (#63286) →

Cayley diagram

C2×C3×D23 #63285

order276
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D23
unambiguous semidirect productC23⋊(C22×C3)
unambiguous semidirect product(C2×C23)⋊(C2×C3)

Splittings

Fitting, socleC2×C3×C23 ⋊ C2
derived, SylowC23 ⋊ C22×C3
HallC3×C23 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C3D23
commutator, cosocle, hypocenterC23C22×C3
FrattiniC1G
Fitting, socleC2×C3×C23C2
LCSG ▷ C23
UCSC1 ◁ C2×C3

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 138

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

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

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic3×D23, #10587770, #10587771, …
maximal normal subgroup ofDic3×D23, #10587770, #10587771, …
maximal quotient ofC3×Dic46, C3×C4×D23, C3×D92, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(276, 7);