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Cayley diagram

C13×M16 #6113

order208
nilpotency class2
isoclinismisoclinic class of D4
automorphismAut(G) = C2×C3×C4×D4 (order 192) · Inn(G) = C22 · Out(G) = C22×C3×C4
homologyAbelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×M16

Subgroups

subgroupG/H
centerC4×C13C22
commutatorC2C2×C4×C13
Frattini, cosocleC4C22×C13
socleC2×C13C2×C4
prime radicalC22×C13C4
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C4×C13 ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 104

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21);(15,19)(17,21)

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of#88062, #88063, #88064, …
maximal subgroup of#88062, #88063, #88064, …
maximal normal subgroup of#88062, #88063, #88064, …
maximal quotient ofC13×#97, C13×C22⋊C8, C13×C4⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(208, 24);