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Cayley diagram

A4×D13 #64634

order312
isoclinismisoclinic class of A4×D13
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C2

Aliases

direct productA4×D13

Splittings

Fitting, socle, derivedC22×C13 ⋊ C2×C3
HallC22×D13 ⋊ C3
SylowC13 ⋊ C2×A4

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C13C2×C3
LCSG ▷ C22×C13
UCSC1

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 52

A minimal faithful permutation representation — 2 generators on 17 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16,17);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,17)(15,16)

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofA4⋊#261, A4×#261, S4×D13, …
maximal normal subgroup ofA4⋊#261, A4×#261, S4×D13, …
maximal quotient of#10597710, SL(2,𝔽3)×D13, A4×Dic13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(312, 50);