Finite Group Databasebeta

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Cayley diagram

C2×Dic44 #66958

order352
isoclinismisoclinic class of #4314
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic44

Splittings

SylowC11 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22D44
commutator, cosocleC4×C11C23
FrattiniC4C22×D11
FittingC2×C8×C11C2
socle, prime radicalC22×C11D4
hypercenterC2×C8D11
hypocenterC11C2×Q16
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 352

A minimal faithful permutation representation — 3 generators on 29 points:

(3,4,6,8,10,12,13,11,9,7,5)(14,16,23,27,18,25,17,24)(15,19,26,29,21,28,20,22);(1,2)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,18,21)(16,22,25,29)(17,26,23,20)(19,27,28,24);(1,2)

Conjugacy classes & character table

94 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10622130, #10622134, #10622141, …
maximal normal subgroup of#10622130, #10622134, #10622141, …
maximal quotient of#10622294, #10622295, C4×Dic44, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 100);