Finite Group Databasebeta

← Prev (#10587180) Next (#10587182) →

C11×Dic12 #10587181

order528
isoclinismisoclinic class of #204
automorphismAut(G) = C2×C5×D3×AGL(1,ℤ/8) (order 1920) · Inn(G) = D12 · Out(G) = C24×C5
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic12

Splittings

HallC3×C11 ⋊ Q16
SylowC3 ⋊ C11×Q16

Subgroups

subgroupG/H
centerC2×C11D12
commutator, cosocleC3×C4C22×C11
FrattiniC4C2×D3×C11
FittingC3×C8×C11C2
socle, prime radicalC2×C3×C11D4
hypercenterC8×C11D3
hypocenterC3C11×Q16
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C11 ◁ C4×C11 ◁ C8×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 528

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19)(20,27,26,25,24,23,22,21)(28,29,30);(12,20,16,24)(13,21,17,25)(14,22,18,26)(15,23,19,27)(29,30)

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11760477, #11760482, #11760483, …
maximal normal subgroup of#11760477, #11760482, #11760483, …
maximal quotient ofC11×#818, C11×#816, C2×C11×Dic12, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 51);