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Cayley diagram

C22×Dic23 #67293

order368
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×Dic23

Splittings

derived, SylowC23 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC23D23
commutator, hypocenterC23C22×C4
FrattiniC2C22×D23
Fitting, socle, prime radicalC23×C23C2
cosocleC2×C23C23
LCSG ▷ C23
UCSC1 ◁ C23

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 368

A minimal faithful permutation representation — 3 generators on 31 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);(3,4)(9,10,12,14,16,18,20,22,24,26,28,30,31,29,27,25,23,21,19,17,15,13,11);(1,2)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23⋊#95, #10625048, #10625049, …
maximal normal subgroup ofC23⋊#95, #10625048, #10625049, …
maximal quotient ofC22×C23⋊C8, C2×#67267, C2×C4×Dic23, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(368, 35);