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Cayley diagram

C22×Dic31 #92500

order496
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×Dic31

Splittings

derived, SylowC31 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC23D31
commutator, hypocenterC31C22×C4
FrattiniC2C22×D31
Fitting, socle, prime radicalC23×C31C2
cosocleC2×C31C23
LCSG ▷ C31
UCSC1 ◁ C23

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 496

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC31⋊#95, #11758454, #11758455, …
maximal normal subgroup ofC31⋊#95, #11758454, #11758455, …
maximal quotient ofC22×C31⋊C8, C2×#92474, C2×C4×Dic31, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(496, 35);