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C13⋊C3×Dic23 #16813262

order3588
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×Dic23
unambiguous semidirect productC23⋊(C4×C13⋊C3)
unambiguous semidirect product(C13×Dic23)⋊C3

Splittings

derived, HallC13×C23 ⋊ C3×C4
HallC13×Dic23 ⋊ C3
HallC23×C13⋊C3 ⋊ C4
SylowC23 ⋊ C4×C13⋊C3
SylowC13 ⋊ C3×Dic23

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C13⋊C3×D23
commutator, hypocenterC13×C23C3×C4
Fitting, socle, cosocleC2×C13×C23C2×C3
prime radicalC2×C23×C13⋊C3C2
LCSG ▷ C13×C23
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 1196

A minimal faithful permutation representation — 2 generators on 40 points:

(2,3,5)(4,7,10)(6,9,8)(11,13,12)(14,15)(16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40);(1,2,4,3,6,10,7,11,13,5,8,12,9)(14,16,15,17)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13⋊C3×Dic23, C13⋊C3×Dic115, C13⋊C3×C23⋊AGL(1,𝔽5), …
maximal normal subgroup ofC5×C13⋊C3×Dic23, C7×C13⋊C3×Dic23
maximal quotient ofC5×C13⋊C3×Dic23, C13⋊C3×Dic115, C13⋊C3×C23⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3588, 2);